Simulace.info - User contributions [en]

Course materials

2023-02-01T19:03:12Z

Kane02:

Please, read the article [[How to write a term paper]] for the hints for writing your semestral paper. '''Make sure''' that your assignment is really writing a course material, not a Wikipedia article! Wikipedia article is to be submitted always and exclusively directly into Wikipedia!

==Materials online==
*[[Monte Carlo method]]
**[[Pseudorandom number generators]]
**[[Randomness tests]]
**[[Probability distributions]]
**[[Variance reduction]]
**[[Monte Carlo method in simulations]]
**[[Interpretation of MC simulation results (Stochastic methods)]]
*[[Discrete event simulation]]
**[[Queueing theory]]
**[[Simulation in Quality management]]
*[[Game theory]]
**[[Nash equilibrium]]
***[[Mixed strategy]]
**[[One-shot games]]
***[[Normal form]]
***[[Prisoner's dilemma]]
***[[The Chicken Game]]
**[[Repeated games]]
**[[Multistage Games]]
***[[Extensive form]]
**[[Multiplayer games]]
***[[Auctions]]
****[[Vickrey's auction]]
***[[N-player prisoner's dilemma]]
***[[Multiplayer cooperative games]]
*[[Multi-agent systems]]
**[[Agents]]
***[[Agent reasoning]]
****[[Markov decision process]]
**[[Agent Environments]]
*[[System Dynamics]]
**[[Causal loop diagram]]
**[[Stock and flow diagram]]
**[[Leverage point]]
**[[System Archetypes]]
***[[Tragedy of the commons]]
***[[Growth and Underinvestment]]
***[[Limits to Growth]]
***[[Shifting the Burden]]
***[[Fixes That Fail]]
***[[Drifting Goals]]
*[[Serious Gaming]]
**[[Virtual reality and serious games]]
==Required reading==
* Šalamon, T. (2011). [http://www.designofagentbasedmodels.info ''Design of Agent-Based Models : Developing Computer Simulations for a Better Understanding of Social Processes'']. Řepín, Czech Republic: Bruckner Publishing

==Recommended reading==
* Colman, A. M. (1982). ''Game theory and experimental games : the study of strategic interaction''. Oxford, UK: Pergamon
* Sterman, J. (2000). ''Business dynamics : systems thinking and modeling for a complex world''. Boston, Ma.: Irwin/McGraw-Hill
* Wooldridge, M. J. (2002). ''An introduction to multiagent systems''. Chichester, UK: John Wiley & Sons
* Polak, B. (2007) ''Game Theory'' In: Yale University: Open Yale Courses, [http://oyc.yale.edu/economics/econ-159 http://oyc.yale.edu/]

Rubinstein Bargaining

2023-02-01T19:02:50Z

Kane02: Blanked the page

File:Kane02.nlogo

2023-01-23T19:40:32Z

Kane02:

Car Park Solution for a New Cinema

2023-01-23T19:40:21Z

Kane02:

Introduction

=Problem definition=

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

=Method=

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

=Model=

Model is created based on business requirements by the owners including all parameters used and developed. To calculate reliability and feasibility simulation goes parallel with profit value which is set by the owners.

'''Here are the things can be visualized:'''
*Wellfare and Overall Price
[[File:netlogo park2.png|500px]]
*Day and mean calculations
[[File:netlogo park3.png|500px]]

'''Simulation Control Options:'''
*Adjusting the price
[[File:netlogo park4.png|500px]]
*Randomize the starting point
[[File:netlogo park5.png|500px]]

=Parameters=

1. Park Timer

a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing

a. Set up rates per hours
b. Conditions on specific days

=How to Use the Program=
Setup button to put the inital settings and go button to start the simulation, also including a step button which ticks once on every click.
There is also start with a random seed value, it triggers when the random start option is off.

[[File:netlogo park6.png|500px]]

=Simulation File=

This zip folder contains the Netlogo simulation

[[File:Kane02.nlogo]]

File:Kanat Efecan Parking.zip

2023-01-23T19:11:47Z

Kane02: Kane02 uploaded a new version of File:Kanat Efecan Parking.zip

Car Park Solution for a New Cinema

2023-01-23T19:11:16Z

Kane02:

Car Park Solution for a New Cinema

2023-01-23T19:01:39Z

Kane02:

File:Kanat Efecan Parking.zip

2023-01-23T19:01:00Z

Kane02: Kane02 uploaded a new version of File:Kanat Efecan Parking.zip

File:Kanat Efecan Parking.zip

2023-01-23T18:47:29Z

Kane02: Kane02 uploaded a new version of File:Kanat Efecan Parking.zip

Car Park Solution for a New Cinema

2023-01-23T18:44:25Z

Kane02:

Car Park Solution for a New Cinema

2023-01-23T18:44:02Z

Kane02:

File:Kanat Efecan Parking.zip

2023-01-23T18:43:20Z

Kane02:

Car Park Solution for a New Cinema

2023-01-23T18:39:33Z

Kane02:

Car Park Solution for a New Cinema

2023-01-23T18:39:09Z

Kane02:

Car Park Solution for a New Cinema

2023-01-23T18:38:42Z

Kane02:

Introduction

=Problem definition=

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

=Method=

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

=Model=

Model is created based on business requirements by the owners including all parameters used and developed. To calculate reliability and feasibility simulation goes parallel with profit value which is set by the owners.

'''Here are the things can be visualized:'''
*Wellfare and Overall Price
[[File:netlogo park2.png|200px]]
*Day and mean calculations
[[File:netlogo park3.png]]

'''Simulation Control Options:'''
*Adjusting the price
[[File:netlogo park4.png]]
*Randomize the starting point
[[File:netlogo park5.png]]

=Parameters=

1. Park Timer

a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing

a. Set up rates per hours
b. Conditions on specific days

=How to Use the Program=
Setup button to put the inital settings and go button to start the simulation, also including a step button which ticks once on every click.
There is also start with a random seed value, it triggers when the random start option is off.
[[File:netlogo park6.png]]

File:Netlogo park4.png

2023-01-23T18:36:43Z

Kane02: Kane02 uploaded a new version of File:Netlogo park4.png

File:Netlogo park4.png

2023-01-23T18:34:28Z

Kane02: Kane02 uploaded a new version of File:Netlogo park4.png

File:Netlogo park3.png

2023-01-23T18:34:07Z

Kane02: Kane02 uploaded a new version of File:Netlogo park3.png

File:Netlogo park2.png

2023-01-23T18:33:39Z

Kane02: Kane02 uploaded a new version of File:Netlogo park2.png

Car Park Solution for a New Cinema

2023-01-23T18:30:08Z

Kane02:

Introduction

=Problem definition=

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

=Method=

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

=Model=

Model is created based on business requirements by the owners including all parameters used and developed. To calculate reliability and feasibility simulation goes parallel with profit value which is set by the owners.

'''Here are the things can be visualized:'''
*Wellfare and Overall Price
[[File:netlogo park2.png]|500px|center]]
*Day and mean calculations
[[File:netlogo park3.png]]

'''Simulation Control Options:'''
*Adjusting the price
[[File:netlogo park4.png]]
*Randomize the starting point
[[File:netlogo park5.png]]

=Parameters=

1. Park Timer

a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing

a. Set up rates per hours
b. Conditions on specific days

=How to Use the Program=
Setup button to put the inital settings and go button to start the simulation, also including a step button which ticks once on every click.
There is also start with a random seed value, it triggers when the random start option is off.
[[File:netlogo park6.png]]

Car Park Solution for a New Cinema

2023-01-23T18:27:50Z

Kane02:

Introduction

=Problem definition=

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

=Method=

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

=Model=

Model is created based on business requirements by the owners including all parameters used and developed. To calculate reliability and feasibility simulation goes parallel with profit value which is set by the owners.

'''Here are the things can be visualized:'''
*Wellfare and Overall Price
[[File:netlogo park2.png]|350px]]
*Day and mean calculations
[[File:netlogo park3.png]]

'''Simulation Control Options:'''
*Adjusting the price
[[File:netlogo park4.png]]
*Randomize the starting point
[[File:netlogo park5.png]]

=Parameters=

1. Park Timer

a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing

a. Set up rates per hours
b. Conditions on specific days

=How to Use the Program=
Setup button to put the inital settings and go button to start the simulation, also including a step button which ticks once on every click.
There is also start with a random seed value, it triggers when the random start option is off.
[[File:netlogo park6.png]]

Car Park Solution for a New Cinema

2023-01-23T18:27:23Z

Kane02:

Introduction

=Problem definition=

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

=Method=

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

=Model=

Model is created based on business requirements by the owners including all parameters used and developed. To calculate reliability and feasibility simulation goes parallel with profit value which is set by the owners.

'''Here are the things can be visualized:'''
*Wellfare and Overall Price
[[File:netlogo park2.png]|350px]
*Day and mean calculations
[[File:netlogo park3.png]]

'''Simulation Control Options:'''
*Adjusting the price
[[File:netlogo park4.png]]
*Randomize the starting point
[[File:netlogo park5.png]]

=Parameters=

1. Park Timer

a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing

a. Set up rates per hours
b. Conditions on specific days

=How to Use the Program=
Setup button to put the inital settings and go button to start the simulation, also including a step button which ticks once on every click.
There is also start with a random seed value, it triggers when the random start option is off.
[[File:netlogo park6.png]]

File:Netlogo park6.png

2023-01-23T18:26:54Z

Kane02:

Car Park Solution for a New Cinema

2023-01-23T18:26:01Z

Kane02:

Introduction

=Problem definition=

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

=Method=

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

=Model=

Model is created based on business requirements by the owners including all parameters used and developed. To calculate reliability and feasibility simulation goes parallel with profit value which is set by the owners.

'''Here are the things can be visualized:'''
*Wellfare and Overall Price
[[File:netlogo park2.png]]
*Day and mean calculations
[[File:netlogo park3.png]]

'''Simulation Control Options:'''
*Adjusting the price
[[File:netlogo park4.png]]
*Randomize the starting point
[[File:netlogo park5.png]]

=Parameters=

1. Park Timer

a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing

a. Set up rates per hours
b. Conditions on specific days

=How to Use the Program=
Setup button to put the inital settings and go button to start the simulation, also including a step button which ticks once on every click.
There is also start with a random seed value, it triggers when the random start option is off.
[[File:netlogo park6.png]]

File:Netlogo park1.png

2023-01-23T18:24:14Z

Kane02:

File:Netlogo park5.png

2023-01-23T18:23:51Z

Kane02:

File:Netlogo park4.png

2023-01-23T18:23:40Z

Kane02:

File:Netlogo park3.png

2023-01-23T18:23:19Z

Kane02:

File:Netlogo park2.png

2023-01-23T18:22:52Z

Kane02:

Car Park Solution for a New Cinema

2023-01-23T18:22:22Z

Kane02: Created page with "Introduction =Problem definition= A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their..."

Introduction

=Problem definition=

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

=Method=

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

=Model=

Model is created based on business requirements by the owners including all parameters used and developed. To calculate reliability and feasibility simulation goes parallel with profit value which is set by the owners.

'''Here are the things can be visualized:'''
*Wellfare and Overall Price
[[File:netlogo park2.png]]
*Day and mean calculations
[[File:netlogo park3.png]]

'''Simulation Control Options:'''
*Adjusting the price
[[File:netlogo park4.png]]
*Randomize the starting point
[[File:netlogo park5.png]]

=Parameters=

1. Park Timer

a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing

a. Set up rates per hours
b. Conditions on specific days

=How to Use the Program=
Setup button to put the inital settings and go button to start the simulation, also including a step button which ticks once on every click.
There is also start with a random seed value, it triggers when the random start option is off.
[[File:netlogo park1.png]]

WS 2022/2023

2023-01-23T17:54:00Z

Kane02:

Semestral papers from winter term 2022/2023. Please, put here links to the pages with your paper. First you need to have your [[Assignments WS 2022/2023|assignment approved]]

==Simulations==
--[[User:Julian Bleyer|Julian Bleyer]] ([[User talk:Xkrep33|talk]]) 0:44, 18 January 2023(CET) Aircraft Evacuation Simulation: [[Airplane_Evacuation]]

--[[User:Baumareb|Baumareb]] ([[User talk:Baumareb|talk]]) 13:55, 18 January 2023 (CET) Cartel simulation with leniency program by Rebecca Baumann (baur00): [[cartel_simulation]]

--[[User:Kock06|Kock06]] ([[User talk:Kock06|talk]]) 14:03, 22 January(GTM+8) Receivables prediction by Monte Carlo simulation: [[Receivables]]

--[[User:Ruzv01|Ruzv01]] ([[User talk:Ruzv01|talk]]) 10:33, 22 January(CET) Household electricity consumption: [[Household electricity consumption]]

--[[User:Haki00|Haki00]] ([[User talk:Haki00|talk]]) 21:38, 22 January(CET) Artsakh blockade: [[Artsakh blockade]]

--[[User:Edema|Edema]] ([[User talk:Haki00|talk]]) 22:00, 22 January(CET) Mortgage Assessment: [[Mortgage Assessment]]

--[[User:BortnikSvitlana|BortnikSvitlana]] ([[User talk:BortnikSvitlana|talk]]) 22:36, 22 January(CET) Traffic Simulation at an Intersection: [[Traffic Simulation at an Intersection]]

--[[User:Ceta|Ceta]] ([[User talk:Ceta|talk]]) 22:48, 22 January 2023 (CET) Pumped hydroelectric energy storage (PHES)System Simulation [[Pump_storage]]

--[[User:Botd00|Botd00]] ([[User talk:Botd00|talk]]) 22:46, 22 January(CET) Twitter Simulation: [[Twitter simulation]]

-- [[User:Miln02|Miln02]] ([[User talk:Miln02|talk]]) 23:05, 22 January 2023 (CET) Saving for an apartment [[Savingforanapartment]]

-- [[User:Abizah1|Abizah1]] ([[User talk:Abizah1|talk]]) 23:55, 22 January 2023 (CET) https://www.simulace.info/index.php/Boxing_athlete

-- [[User:Pierreatekwana1|Pierreatekwana1]] ([[User talk:Pierreatekwana1|talk]]) 00:24, 23 January 2023 (CET) Crop yield simulation: [[Cropyield]]

-- [[User:Kane02|Kane02]] ([[User talk:Kane02|talk]]) 18:52, 23 January 2023 (CET) Car Park Solution for a New Cinema [[Car Park Solution for a New Cinema]]

Rubinstein Bargaining

2023-01-14T11:24:51Z

Kane02:

=Introduction=

In game theory, the Rubinstein bargaining model is a solution to the problem of finding an optimal agreement between two parties who have conflicting interests and asymmetric information. For example lets just say two parties Bob and Alice, engage in a series of alternating offers and counteroffers on a resource that is valuable to both, until they reach an agreement or until they reach a predetermined deadline. How will they behave or what are the necessary steps must be taken by each player? What are the possibile results in the end of the bargaining? In this chapter you will find further details and deepdives about Rubinstein Bargaining concept and solution.

=Problem Definition=

In the Rubinstein bargaining model, two parties usually referred to as "players," are trying to reach an agreement on the division of a pie, where the pie represents a set of resources that are valuable to both parties. The players have conflicting interests and asymmetric information, meaning they have different preferences over how the pie should be divided, and they need complete information about the other player's choices.
The Rubinstein model is a two-stage game.

In the first stage, each player offers the other player how the resource should be split. In the second stage, the other player can accept the offer, reject it, or make a counteroffer. The game continues with the players making alternating offers and counteroffers until they reach an agreement or until they reach a predetermined deadline.
The players are assumed to be rational and have complete information about their preferences but not about the importance of the other player. The goal of each player is to maximize their utility, which is the measure of their satisfaction or happiness with the outcome of the negotiation. The Rubinstein model seeks an equilibrium, a stable agreement that either player cannot improve upon<ref name="testrubinstein1">[ An experimental test of Rubinstein's bargaining model
[online]. Available at: https://discovery.ucl.ac.uk/id/eprint/14439/1/14439.pdf]</ref>.

Rubinstein Bargaining game has 3 definitive rules that must be followed through as each stage performed.
* The negotiation begins with an initial offer from one of the parties.
* Initial offer must receive a response in form of either accept, reject, or a counteroffer.
* Bargaing must end with either an agreement is reached or a predetermined timeout deadline is set<ref name="testrubinstein2">[ A Course in Game Theory 2012 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/books/GT.pdf]</ref>.

'''Fact:''' The model does not specify a fixed number of stages or a fixed deadline, and the actual number of stages and the length of the negotiation will depend on the specific circumstances of the negotiation.

=Parameters=
The key parameters in the Rubinstein model are the time discount factor and the reservation value<ref name="testrubinstein3">[ Rubinstein’s bargaining model 2018 [cit. 2023-01-11] [online]. Available at: http://diposit.ub.edu/dspace/bitstream/2445/176605/1/TFG_Francisca_Gaya_16809785%282%29.pdf]</ref>.

'''Set of Ordered Pairs:''' The set of ordered pairs is denoted by (s, t), where (s, t) is the discrete representation of time and (s, t) represents a slice of a pie with size 1. Hence, t > 0. Therefore, the pair says, "Player 1 receives s and Player 2 receives 1 - s at time t. The following prerequisites should be met by each player's preferences on (s, t):

'''More Pie or Resource: ''' The best pie is more pie. According to math, if x > y, then (x, t) > (y, t).

'''Time is Money: ''' This indicates that if x > 0 and t2 > t1, then (x, t1) > (x, t2).

'''Continuity: ''' Thus, there are no sudden changes in people's tastes. In terms of mathematics, a preference relation is continuous, In other words, points very near to A will also be preferred to B if we prefer a point A along a preference curve to a point B.

'''Stationary: '''This means that the preference of (x, t) over (y, t + 1) is independent of t.

'''Time Discount Factor:''' The time discount factor represents the degree to which the parties value a settlement reached sooner rather than later. A high-time discount factor means that the parties place a high value on getting an agreement quickly, while a low-time discount factor means they are willing to wait for a more favorable settlement. The time discount factor is often expressed as a decimal between 0 and 1, with higher values indicating a greater preference for settlements reached sooner rather than later. For example, a time discount factor of 0.9 means that the parties place a high value on reaching an agreement quickly, while a time discount factor of 0.1 means that they are willing to wait for a more favorable settlement. So, if (x, t) is equivalent to (y, t + 1) then y needs to be bigger than x to continue one more period with the bargaining and being immaterial to him.

'''Reservation Value:''' The reservation value is the minimum amount of resources that each party is willing to accept in the settlement. If either party's reservation value is not met, they will not agree to the settlement and the negotiation will break down. The reservation value can be thought of as a "fallback" position for each party. If the negotiation breaks down and an agreement is not reached, each party will receive their reservation value rather than nothing. For this reason, the reservation value is often referred to as the "walkaway" value or the "outside option.

=Nash Equilibrium Condition=

[https://www.simulace.info/index.php/Nash_equilibrium Nash Equilibrium] is a solution concept in game theory, which describes a state in which all players in a game are making the best decision they can given the decisions of the other players. The relation between Rubinstein bargaining and Nash equilibrium is that a Nash equilibrium can be reached through the process of Rubinstein bargaining. In other words, if the agents in a negotiation are rational and have complete information, they will eventually reach a Nash equilibrium through the process of making offers and counter-offers <ref name="testrubinstein4">[ A Course in Game Theory 2012 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/books/GT.pdf]</ref>.

=Benefits of Rubinstein Bargaining=

The Rubinstein bargaining model has several benefits and positives:

1. It provides a framework for understanding how rational agents will behave in a negotiation and can be utilized to forecast the results of a negotiation.

2. Allows for calculating the Nash Bargaining Solution, a unique and efficient solution for both parties involved in the negotiation.

3. Helps to identify the optimal outcome for both parties involved in the negotiation, which can lead to mutually beneficial agreements.

4. Applicable to various negotiation scenarios, making it a versatile tool for understanding negotiations.

5. Can be used to identify potential sources of conflict and design negotiation strategies to mitigate or avoid them.

6. It is used to understand the role of different factors, such as the outside options and reservation values, in the negotiation process.

7. Researchers have extensively studied and validated it, providing a solid theoretical foundation for its use in real-world negotiations.

=Rubinstein Bargaining and Nash Bargaining Solution=

Rubinstein bargaining model can be used to calculate the Nash bargaining solution, it is not the only way to do so, and the relationship between the two models is somewhat complex. The Nash bargaining solution is a theoretical concept that describes the outcome of a negotiation in which both agents are making their best decisions given the decisions of the other agent. It can be derived from the Nash equilibrium, a state in which all players in a game are making the best decision they can, given the findings of the other players<ref name="testrubinstein5">[ Game Theory An Introduction 2013 [cit. 2023-01-11] [online]. Available at: http://students.aiu.edu/submissions/profiles/resources/onlineBook/Y5z2A2_Game_Theory_An_Introduction.pdf]</ref>.
The Rubinstein bargaining model is a more specific negotiation model that considers the agents' time discounting and complete information. The Nash bargaining solution, however, does not make any assumptions about the agents' preferences or information and does not consider the surplus's time discounting.

=General Solution=

The solution of the Rubinstein bargaining model is determined by the following formulas:

1. The first formula is for the time-discounted value of the surplus, which is used to calculate the value of an agreement as time passes<ref name="testrubinstein6">[ Perfect Equilibrium in a Bargaining Model 1982 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/papers/11.pdf]</ref>. The formula is:
V(t) = S / (1 + d*t)
Where:
* V(t) is the time-discounted value of the surplus
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
* t is the time elapsed since the beginning of the negotiation
2. The second formula is for the disagreement point, which represents the value of the best alternative for each agent if they don't reach an agreement. The formula is:
D = (1- d) * S
Where:
* D is the disagreement point
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
3. The third formula is for the Rubinstein bargaining solution, which describes the division of the surplus between the two agents. The formula is:
x = D + (S - D) * (b1 / (b1 + b2))
Where:
* x is the share of the surplus that goes to the first agent
* D is the disagreement point
* S is the total surplus
* b1 and b2 are the bargaining power of the agents, where a high value of b indicates that one agent has more bargaining power than the other.

It's important to notice that this model is a simplified version of the bargaining process, in the real world the negotiation process can be more complicated and factors such as the agents' emotions, trust and communication can affect the outcome.

=Rubinstein Bargaining Game Examples=

A quick and simple example about Rubinstein Barganing game:

'''Game Example 1: '''

A landlord and the tenant bargains over the price of rent. The landlord and the tenant have a common objective of reaching a rental agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

The tenant's outside option is to rent a similar property at a different location, while the landlord's outside option is to keep the property vacant. The potential surplus in this negotiation is the difference between the landlord's profit with a tenant and without a tenant.

The payoffs for each party can be represented by the following formulas:

Tenant: uT(r) = r - r0

Landlord: uL(r) = r - r0 - c

Where r is the agreed rent, r0 is the tenant's reservation price, and c is the landlord's cost of keeping the property vacant.

The Nash Bargaining Solution can be calculated using the following formula:

r = (r0 + c)/2 + (r0 - c)/2 = (r0 + c)

This means that the tenant and the landlord will agree on a rent that is halfway between the tenant's reservation price and the landlord's cost of keeping the property vacant.

For example, if the tenant's reservation price is $1000 and the landlord's cost of keeping the property vacant is $800, the Nash Bargaining Solution is:

r = ($1000 + $800)/2 = $900

This means that the tenant and the landlord will agree on a rent of $900, and both parties will be better off than their outside options. The tenant will be paying less than their reservation price, while the landlord will be earning more than their cost of keeping the property vacant.

'''Game Example 2: '''
This example is about the negotiation process between a buyer and a seller over the price of a car with using Rubinstein Bargaining Solution. The buyer and the seller have a common objective of reaching a sale agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

[[File:car bargaining.jpeg|500px|center]]

The buyer's outside option is to purchase a similar car from a different seller, while the seller's outside option is to keep the car unsold. The potential surplus in this negotiation is the difference between the seller's profit from selling the car and keeping it unsold.

The payoffs for each party can be represented by the following formulas:

Buyer: uB(p) = p - p0

Seller: uS(p) = p - c - p0

Where p is the agreed price, p0 is the buyer's reservation price, and c is the seller's cost of keeping the car unsold.

The Nash Bargaining Solution can be calculated using the following formula:

p = (p0 + c)/2 + (p0 - c)/2 = (p0 + c)

This means that the buyer and the seller will agree on a price that is halfway between the buyer's reservation price and the seller's cost of keeping the car unsold.

For example, if the buyer's reservation price is $15,000 and the seller's cost of keeping the car unsold is $12,000, the Nash Bargaining Solution is:

p = ($15,000 + $12,000)/2 = $13,500

This means that the buyer and the seller will agree on a price of $13,500, and both parties will be better off than their outside options. The buyer will be paying less than their reservation price, while the seller will be earning more than their cost of keeping the car unsold.

=Relevency of Rubinstein Bargaining=

Rubinstein's bargaining is utilized in various fields, including economics, political science, and management. In economics, the model is used to study the market negotiation process and understand the role of information in shaping market outcomes. In political science, the model is used to study the negotiation process in international relations and understand power's role in shaping outcomes. In management, the model is used to study the negotiation process in organizations and to know how different types of administration affect the outcome of negotiations<ref name="testrubinstein7">[ Behavioural Economics: Theory and Evidence on Bargaining 2013 [cit. 2023-01-11] [online]. Available at: https://econweb.ucsd.edu/~vcrawfor/BGTBargainingSlides13.pdf]</ref>.
In economics, the Rubinstein bargaining theory helps to understand how prices are shaped in markets and how changes in supply and demand affect the price. In international relations, the approach is used to know how countries negotiate treaties and agreements.
In practice, Rubinstein bargaining is also used to study the negotiation process in different sectors, such as labor negotiation, mergers and acquisitions, and international trade<ref name="testrubinstein8">[ Game Theory An Introduction 2013 [cit. 2023-01-11] [online]. Available at: http://students.aiu.edu/submissions/profiles/resources/onlineBook/Y5z2A2_Game_Theory_An_Introduction.pdf]</ref>.

=References=
<references/>

Rubinstein Bargaining

2023-01-14T11:23:11Z

Kane02:

Rubinstein Bargaining

2023-01-14T11:16:27Z

Kane02:

=Introduction=

In game theory, the Rubinstein bargaining model is a solution to the problem of finding an optimal agreement between two parties who have conflicting interests and asymmetric information. For example lets just say two parties Bob and Alice, engage in a series of alternating offers and counteroffers on a resource that is valuable to both, until they reach an agreement or until they reach a predetermined deadline. How will they behave or what are the necessary steps must be taken by each player? What are the possibile results in the end of the bargaining? In this chapter you will find further details and deepdives about Rubinstein Bargaining concept and solution.

=Problem Definition=

In the Rubinstein bargaining model, two parties usually referred to as "players," are trying to reach an agreement on the division of a pie, where the pie represents a set of resources that are valuable to both parties. The players have conflicting interests and asymmetric information, meaning they have different preferences over how the pie should be divided, and they need complete information about the other player's choices.
The Rubinstein model is a two-stage game.

In the first stage, each player offers the other player how the resource should be split. In the second stage, the other player can accept the offer, reject it, or make a counteroffer. The game continues with the players making alternating offers and counteroffers until they reach an agreement or until they reach a predetermined deadline.
The players are assumed to be rational and have complete information about their preferences but not about the importance of the other player. The goal of each player is to maximize their utility, which is the measure of their satisfaction or happiness with the outcome of the negotiation. The Rubinstein model seeks an equilibrium, a stable agreement that either player cannot improve upon<ref name="testrubinstein1">[ An experimental test of Rubinstein's bargaining model
[online]. Available at: https://discovery.ucl.ac.uk/id/eprint/14439/1/14439.pdf]</ref>.

Rubinstein Bargaining game has 3 definitive rules that must be followed through as each stage performed.
* The negotiation begins with an initial offer from one of the parties.
* Initial offer must receive a response in form of either accept, reject, or a counteroffer.
* Bargaing must end with either an agreement is reached or a predetermined timeout deadline is set<ref name="testrubinstein2">[ A Course in Game Theory 2012 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/books/GT.pdf]</ref>.

'''Fact:''' The model does not specify a fixed number of stages or a fixed deadline, and the actual number of stages and the length of the negotiation will depend on the specific circumstances of the negotiation.

=Parameters=
The key parameters in the Rubinstein model are the time discount factor and the reservation value<ref name="testrubinstein3">[ Rubinstein’s bargaining model 2018 [cit. 2023-01-11] [online]. Available at: http://diposit.ub.edu/dspace/bitstream/2445/176605/1/TFG_Francisca_Gaya_16809785%282%29.pdf]</ref>.

'''Set of Ordered Pairs:''' The set of ordered pairs is denoted by (s, t), where (s, t) is the discrete representation of time and (s, t) represents a slice of a pie with size 1. Hence, t > 0. Therefore, the pair says, "Player 1 receives s and Player 2 receives 1 - s at time t. The following prerequisites should be met by each player's preferences on (s, t):

'''More Pie or Resource: ''' The best pie is more pie. According to math, if x > y, then (x, t) > (y, t).

'''Time is Money: ''' This indicates that if x > 0 and t2 > t1, then (x, t1) > (x, t2).

'''Continuity: ''' Thus, there are no sudden changes in people's tastes. In terms of mathematics, a preference relation is continuous, In other words, points very near to A will also be preferred to B if we prefer a point A along a preference curve to a point B.

'''Stationary: '''This means that the preference of (x, t) over (y, t + 1) is independent of t.

'''Time Discount Factor:''' The time discount factor represents the degree to which the parties value a settlement reached sooner rather than later. A high-time discount factor means that the parties place a high value on getting an agreement quickly, while a low-time discount factor means they are willing to wait for a more favorable settlement. The time discount factor is often expressed as a decimal between 0 and 1, with higher values indicating a greater preference for settlements reached sooner rather than later. For example, a time discount factor of 0.9 means that the parties place a high value on reaching an agreement quickly, while a time discount factor of 0.1 means that they are willing to wait for a more favorable settlement. So, if (x, t) is equivalent to (y, t + 1) then y needs to be bigger than x to continue one more period with the bargaining and being immaterial to him.

'''Reservation Value:''' The reservation value is the minimum amount of resources that each party is willing to accept in the settlement. If either party's reservation value is not met, they will not agree to the settlement and the negotiation will break down. The reservation value can be thought of as a "fallback" position for each party. If the negotiation breaks down and an agreement is not reached, each party will receive their reservation value rather than nothing. For this reason, the reservation value is often referred to as the "walkaway" value or the "outside option.

=Nash Equilibrium Condition=

[https://www.simulace.info/index.php/Nash_equilibrium Nash Equilibrium] is a solution concept in game theory, which describes a state in which all players in a game are making the best decision they can given the decisions of the other players. The relation between Rubinstein bargaining and Nash equilibrium is that a Nash equilibrium can be reached through the process of Rubinstein bargaining. In other words, if the agents in a negotiation are rational and have complete information, they will eventually reach a Nash equilibrium through the process of making offers and counter-offers <ref name="testrubinstein4">[ A Course in Game Theory 2012 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/books/GT.pdf]</ref>.

=Benefits of Rubinstein Bargaining=

The Rubinstein bargaining model has several benefits and positives:

1. It provides a framework for understanding how rational agents will behave in a negotiation and can be utilized to forecast the results of a negotiation.

2. Allows for calculating the Nash Bargaining Solution, a unique and efficient solution for both parties involved in the negotiation.

3. Helps to identify the optimal outcome for both parties involved in the negotiation, which can lead to mutually beneficial agreements.

4. Applicable to various negotiation scenarios, making it a versatile tool for understanding negotiations.

5. Can be used to identify potential sources of conflict and design negotiation strategies to mitigate or avoid them.

6. It is used to understand the role of different factors, such as the outside options and reservation values, in the negotiation process.

7. Researchers have extensively studied and validated it, providing a solid theoretical foundation for its use in real-world negotiations.

=Rubinstein Bargaining and Nash Bargaining Solution=

Rubinstein bargaining model can be used to calculate the Nash bargaining solution, it is not the only way to do so, and the relationship between the two models is somewhat complex. The Nash bargaining solution is a theoretical concept that describes the outcome of a negotiation in which both agents are making their best decisions given the decisions of the other agent. It can be derived from the Nash equilibrium, a state in which all players in a game are making the best decision they can, given the findings of the other players<ref name="testrubinstein5">[ Game Theory An Introduction 2013 [cit. 2023-01-11] [online]. Available at: http://students.aiu.edu/submissions/profiles/resources/onlineBook/Y5z2A2_Game_Theory_An_Introduction.pdf]</ref>.
The Rubinstein bargaining model is a more specific negotiation model that considers the agents' time discounting and complete information. The Nash bargaining solution, however, does not make any assumptions about the agents' preferences or information and does not consider the surplus's time discounting.

=General Solution=

The solution of the Rubinstein bargaining model is determined by the following formulas:

1. The first formula is for the time-discounted value of the surplus, which is used to calculate the value of an agreement as time passes<ref name="testrubinstein6">[ Perfect Equilibrium in a Bargaining Model 1982 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/papers/11.pdf]</ref>. The formula is:
V(t) = S / (1 + d*t)
Where:
* V(t) is the time-discounted value of the surplus
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
* t is the time elapsed since the beginning of the negotiation
2. The second formula is for the disagreement point, which represents the value of the best alternative for each agent if they don't reach an agreement. The formula is:
D = (1- d) * S
Where:
* D is the disagreement point
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
3. The third formula is for the Rubinstein bargaining solution, which describes the division of the surplus between the two agents. The formula is:
x = D + (S - D) * (b1 / (b1 + b2))
Where:
* x is the share of the surplus that goes to the first agent
* D is the disagreement point
* S is the total surplus
* b1 and b2 are the bargaining power of the agents, where a high value of b indicates that one agent has more bargaining power than the other.

It's important to notice that this model is a simplified version of the bargaining process, in the real world the negotiation process can be more complicated and factors such as the agents' emotions, trust and communication can affect the outcome.

=Rubinstein Bargaining Game Examples=

A quick and simple example about Rubinstein Barganing game:

'''Game Example 1: '''

A landlord and the tenant bargains over the price of rent. The landlord and the tenant have a common objective of reaching a rental agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

The tenant's outside option is to rent a similar property at a different location, while the landlord's outside option is to keep the property vacant. The potential surplus in this negotiation is the difference between the landlord's profit with a tenant and without a tenant.

The payoffs for each party can be represented by the following formulas:

Tenant: uT(r) = r - r0

Landlord: uL(r) = r - r0 - c

Where r is the agreed rent, r0 is the tenant's reservation price, and c is the landlord's cost of keeping the property vacant.

The Nash Bargaining Solution can be calculated using the following formula:

r = (r0 + c)/2 + (r0 - c)/2 = (r0 + c)

This means that the tenant and the landlord will agree on a rent that is halfway between the tenant's reservation price and the landlord's cost of keeping the property vacant.

For example, if the tenant's reservation price is $1000 and the landlord's cost of keeping the property vacant is $800, the Nash Bargaining Solution is:

r = ($1000 + $800)/2 = $900

This means that the tenant and the landlord will agree on a rent of $900, and both parties will be better off than their outside options. The tenant will be paying less than their reservation price, while the landlord will be earning more than their cost of keeping the property vacant.

'''Game Example 2: '''
This example is about the negotiation process between a buyer and a seller over the price of a car with using Rubinstein Bargaining Solution. The buyer and the seller have a common objective of reaching a sale agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

[[File:car bargaining.jpeg|500px|center]]

The buyer's outside option is to purchase a similar car from a different seller, while the seller's outside option is to keep the car unsold. The potential surplus in this negotiation is the difference between the seller's profit from selling the car and keeping it unsold.

The payoffs for each party can be represented by the following formulas:

Buyer: uB(p) = p - p0

Seller: uS(p) = p - c - p0

Where p is the agreed price, p0 is the buyer's reservation price, and c is the seller's cost of keeping the car unsold.

The Nash Bargaining Solution can be calculated using the following formula:

p = (p0 + c)/2 + (p0 - c)/2 = (p0 + c)

This means that the buyer and the seller will agree on a price that is halfway between the buyer's reservation price and the seller's cost of keeping the car unsold.

For example, if the buyer's reservation price is $15,000 and the seller's cost of keeping the car unsold is $12,000, the Nash Bargaining Solution is:

p = ($15,000 + $12,000)/2 = $13,500

This means that the buyer and the seller will agree on a price of $13,500, and both parties will be better off than their outside options. The buyer will be paying less than their reservation price, while the seller will be earning more than their cost of keeping the car unsold.

=Relevency of Rubinstein Bargaining=

Rubinstein's bargaining is utilized in various fields, including economics, political science, and management. In economics, the model is used to study the market negotiation process and understand the role of information in shaping market outcomes. In political science, the model is used to study the negotiation process in international relations and understand power's role in shaping outcomes. In management, the model is used to study the negotiation process in organizations and to know how different types of administration affect the outcome of negotiations.
In economics, the Rubinstein bargaining theory helps to understand how prices are shaped in markets and how changes in supply and demand affect the price. In international relations, the approach is used to know how countries negotiate treaties and agreements.
In practice, Rubinstein bargaining is also used to study the negotiation process in different sectors, such as labor negotiation, mergers and acquisitions, and international trade<ref name="testrubinstein7">[ Game Theory An Introduction 2013 [cit. 2023-01-11] [online]. Available at: http://students.aiu.edu/submissions/profiles/resources/onlineBook/Y5z2A2_Game_Theory_An_Introduction.pdf]</ref>.

==References==
<references/>

Rubinstein Bargaining

2023-01-14T11:14:32Z

Kane02:

=Introduction=

In game theory, the Rubinstein bargaining model is a solution to the problem of finding an optimal agreement between two parties who have conflicting interests and asymmetric information. For example lets just say two parties Bob and Alice, engage in a series of alternating offers and counteroffers on a resource that is valuable to both, until they reach an agreement or until they reach a predetermined deadline. How will they behave or what are the necessary steps must be taken by each player? What are the possibile results in the end of the bargaining? In this chapter you will find further details and deepdives about Rubinstein Bargaining concept and solution.

=Problem Definition=

In the Rubinstein bargaining model, two parties usually referred to as "players," are trying to reach an agreement on the division of a pie, where the pie represents a set of resources that are valuable to both parties. The players have conflicting interests and asymmetric information, meaning they have different preferences over how the pie should be divided, and they need complete information about the other player's choices.
The Rubinstein model is a two-stage game.

In the first stage, each player offers the other player how the resource should be split. In the second stage, the other player can accept the offer, reject it, or make a counteroffer. The game continues with the players making alternating offers and counteroffers until they reach an agreement or until they reach a predetermined deadline.
The players are assumed to be rational and have complete information about their preferences but not about the importance of the other player. The goal of each player is to maximize their utility, which is the measure of their satisfaction or happiness with the outcome of the negotiation. The Rubinstein model seeks an equilibrium, a stable agreement that either player cannot improve upon<ref name="testrubinstein">[ An experimental test of Rubinstein's bargaining model
[online]. Available at: https://discovery.ucl.ac.uk/id/eprint/14439/1/14439.pdf]</ref>.

Rubinstein Bargaining game has 3 definitive rules that must be followed through as each stage performed.
* The negotiation begins with an initial offer from one of the parties.
* Initial offer must receive a response in form of either accept, reject, or a counteroffer.
* Bargaing must end with either an agreement is reached or a predetermined timeout deadline is set<ref name="testrubinstein3">[ A Course in Game Theory 2012 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/books/GT.pdf]</ref>.

'''Fact:''' The model does not specify a fixed number of stages or a fixed deadline, and the actual number of stages and the length of the negotiation will depend on the specific circumstances of the negotiation.

=Parameters=
The key parameters in the Rubinstein model are the time discount factor and the reservation value<ref name="testrubinstein2">[ Rubinstein’s bargaining model 2018 [cit. 2023-01-11] [online]. Available at: http://diposit.ub.edu/dspace/bitstream/2445/176605/1/TFG_Francisca_Gaya_16809785%282%29.pdf]</ref>.

'''Set of Ordered Pairs:''' The set of ordered pairs is denoted by (s, t), where (s, t) is the discrete representation of time and (s, t) represents a slice of a pie with size 1. Hence, t > 0. Therefore, the pair says, "Player 1 receives s and Player 2 receives 1 - s at time t. The following prerequisites should be met by each player's preferences on (s, t):

'''More Pie or Resource: ''' The best pie is more pie. According to math, if x > y, then (x, t) > (y, t).

'''Time is Money: ''' This indicates that if x > 0 and t2 > t1, then (x, t1) > (x, t2).

'''Continuity: ''' Thus, there are no sudden changes in people's tastes. In terms of mathematics, a preference relation is continuous, In other words, points very near to A will also be preferred to B if we prefer a point A along a preference curve to a point B.

'''Stationary: '''This means that the preference of (x, t) over (y, t + 1) is independent of t.

'''Time Discount Factor:''' The time discount factor represents the degree to which the parties value a settlement reached sooner rather than later. A high-time discount factor means that the parties place a high value on getting an agreement quickly, while a low-time discount factor means they are willing to wait for a more favorable settlement. The time discount factor is often expressed as a decimal between 0 and 1, with higher values indicating a greater preference for settlements reached sooner rather than later. For example, a time discount factor of 0.9 means that the parties place a high value on reaching an agreement quickly, while a time discount factor of 0.1 means that they are willing to wait for a more favorable settlement. So, if (x, t) is equivalent to (y, t + 1) then y needs to be bigger than x to continue one more period with the bargaining and being immaterial to him.

'''Reservation Value:''' The reservation value is the minimum amount of resources that each party is willing to accept in the settlement. If either party's reservation value is not met, they will not agree to the settlement and the negotiation will break down. The reservation value can be thought of as a "fallback" position for each party. If the negotiation breaks down and an agreement is not reached, each party will receive their reservation value rather than nothing. For this reason, the reservation value is often referred to as the "walkaway" value or the "outside option.

=Nash Equilibrium Condition=

[https://www.simulace.info/index.php/Nash_equilibrium Nash Equilibrium] is a solution concept in game theory, which describes a state in which all players in a game are making the best decision they can given the decisions of the other players. The relation between Rubinstein bargaining and Nash equilibrium is that a Nash equilibrium can be reached through the process of Rubinstein bargaining. In other words, if the agents in a negotiation are rational and have complete information, they will eventually reach a Nash equilibrium through the process of making offers and counter-offers <ref name="testrubinstein4">[ A Course in Game Theory 2012 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/books/GT.pdf]</ref>.

=Benefits of Rubinstein Bargaining=

The Rubinstein bargaining model has several benefits and positives:

1. It provides a framework for understanding how rational agents will behave in a negotiation and can be utilized to forecast the results of a negotiation.

2. Allows for calculating the Nash Bargaining Solution, a unique and efficient solution for both parties involved in the negotiation.

3. Helps to identify the optimal outcome for both parties involved in the negotiation, which can lead to mutually beneficial agreements.

4. Applicable to various negotiation scenarios, making it a versatile tool for understanding negotiations.

5. Can be used to identify potential sources of conflict and design negotiation strategies to mitigate or avoid them.

6. It is used to understand the role of different factors, such as the outside options and reservation values, in the negotiation process.

7. Researchers have extensively studied and validated it, providing a solid theoretical foundation for its use in real-world negotiations.

=Rubinstein Bargaining and Nash Bargaining Solution=

Rubinstein bargaining model can be used to calculate the Nash bargaining solution, it is not the only way to do so, and the relationship between the two models is somewhat complex. The Nash bargaining solution is a theoretical concept that describes the outcome of a negotiation in which both agents are making their best decisions given the decisions of the other agent. It can be derived from the Nash equilibrium, a state in which all players in a game are making the best decision they can, given the findings of the other players<ref name="testrubinstein5">[ Game Theory An Introduction 2013 [cit. 2023-01-11] [online]. Available at: http://students.aiu.edu/submissions/profiles/resources/onlineBook/Y5z2A2_Game_Theory_An_Introduction.pdf]</ref>.
The Rubinstein bargaining model is a more specific negotiation model that considers the agents' time discounting and complete information. The Nash bargaining solution, however, does not make any assumptions about the agents' preferences or information and does not consider the surplus's time discounting.

=General Solution=

The solution of the Rubinstein bargaining model is determined by the following formulas:

1. The first formula is for the time-discounted value of the surplus, which is used to calculate the value of an agreement as time passes<ref name="testrubinstein3">[ Perfect Equilibrium in a Bargaining Model 1982 [cit. 2023-01-11] [online]. Available at: https://arielrubinstein.tau.ac.il/papers/11.pdf]</ref>. The formula is:
V(t) = S / (1 + d*t)
Where:
* V(t) is the time-discounted value of the surplus
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
* t is the time elapsed since the beginning of the negotiation
2. The second formula is for the disagreement point, which represents the value of the best alternative for each agent if they don't reach an agreement. The formula is:
D = (1- d) * S
Where:
* D is the disagreement point
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
3. The third formula is for the Rubinstein bargaining solution, which describes the division of the surplus between the two agents. The formula is:
x = D + (S - D) * (b1 / (b1 + b2))
Where:
* x is the share of the surplus that goes to the first agent
* D is the disagreement point
* S is the total surplus
* b1 and b2 are the bargaining power of the agents, where a high value of b indicates that one agent has more bargaining power than the other.

It's important to notice that this model is a simplified version of the bargaining process, in the real world the negotiation process can be more complicated and factors such as the agents' emotions, trust and communication can affect the outcome.

=Rubinstein Bargaining Game Examples=

A quick and simple example about Rubinstein Barganing game:

'''Game Example 1: '''

A landlord and the tenant bargains over the price of rent. The landlord and the tenant have a common objective of reaching a rental agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

The tenant's outside option is to rent a similar property at a different location, while the landlord's outside option is to keep the property vacant. The potential surplus in this negotiation is the difference between the landlord's profit with a tenant and without a tenant.

The payoffs for each party can be represented by the following formulas:

Tenant: uT(r) = r - r0

Landlord: uL(r) = r - r0 - c

Where r is the agreed rent, r0 is the tenant's reservation price, and c is the landlord's cost of keeping the property vacant.

The Nash Bargaining Solution can be calculated using the following formula:

r = (r0 + c)/2 + (r0 - c)/2 = (r0 + c)

This means that the tenant and the landlord will agree on a rent that is halfway between the tenant's reservation price and the landlord's cost of keeping the property vacant.

For example, if the tenant's reservation price is $1000 and the landlord's cost of keeping the property vacant is $800, the Nash Bargaining Solution is:

r = ($1000 + $800)/2 = $900

This means that the tenant and the landlord will agree on a rent of $900, and both parties will be better off than their outside options. The tenant will be paying less than their reservation price, while the landlord will be earning more than their cost of keeping the property vacant.

'''Game Example 2: '''
This example is about the negotiation process between a buyer and a seller over the price of a car with using Rubinstein Bargaining Solution. The buyer and the seller have a common objective of reaching a sale agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

[[File:car bargaining.jpeg|500px|center]]

The buyer's outside option is to purchase a similar car from a different seller, while the seller's outside option is to keep the car unsold. The potential surplus in this negotiation is the difference between the seller's profit from selling the car and keeping it unsold.

The payoffs for each party can be represented by the following formulas:

Buyer: uB(p) = p - p0

Seller: uS(p) = p - c - p0

Where p is the agreed price, p0 is the buyer's reservation price, and c is the seller's cost of keeping the car unsold.

The Nash Bargaining Solution can be calculated using the following formula:

p = (p0 + c)/2 + (p0 - c)/2 = (p0 + c)

This means that the buyer and the seller will agree on a price that is halfway between the buyer's reservation price and the seller's cost of keeping the car unsold.

For example, if the buyer's reservation price is $15,000 and the seller's cost of keeping the car unsold is $12,000, the Nash Bargaining Solution is:

p = ($15,000 + $12,000)/2 = $13,500

This means that the buyer and the seller will agree on a price of $13,500, and both parties will be better off than their outside options. The buyer will be paying less than their reservation price, while the seller will be earning more than their cost of keeping the car unsold.

=Relevency of Rubinstein Bargaining=

Rubinstein's bargaining is utilized in various fields, including economics, political science, and management. In economics, the model is used to study the market negotiation process and understand the role of information in shaping market outcomes. In political science, the model is used to study the negotiation process in international relations and understand power's role in shaping outcomes. In management, the model is used to study the negotiation process in organizations and to know how different types of administration affect the outcome of negotiations.
In economics, the Rubinstein bargaining theory helps to understand how prices are shaped in markets and how changes in supply and demand affect the price. In international relations, the approach is used to know how countries negotiate treaties and agreements.
In practice, Rubinstein bargaining is also used to study the negotiation process in different sectors, such as labor negotiation, mergers and acquisitions, and international trade<ref name="testrubinstein6">[ Game Theory An Introduction 2013 [cit. 2023-01-11] [online]. Available at: http://students.aiu.edu/submissions/profiles/resources/onlineBook/Y5z2A2_Game_Theory_An_Introduction.pdf]</ref>.

Rubinstein Bargaining

2023-01-14T10:45:28Z

Kane02:

=Introduction=

In game theory, the Rubinstein bargaining model is a solution to the problem of finding an optimal agreement between two parties who have conflicting interests and asymmetric information. For example lets just say two parties Bob and Alice, engage in a series of alternating offers and counteroffers on a resource that is valuable to both, until they reach an agreement or until they reach a predetermined deadline. How will they behave or what are the necessary steps must be taken by each player? What are the possibile results in the end of the bargaining? In this chapter you will find further details and deepdives about Rubinstein Bargaining concept and solution.

=Problem Definition=

In the Rubinstein bargaining model, two parties usually referred to as "players," are trying to reach an agreement on the division of a pie, where the pie represents a set of resources that are valuable to both parties. The players have conflicting interests and asymmetric information, meaning they have different preferences over how the pie should be divided, and they need complete information about the other player's choices.
The Rubinstein model is a two-stage game.

In the first stage, each player offers the other player how the resource should be split. In the second stage, the other player can accept the offer, reject it, or make a counteroffer. The game continues with the players making alternating offers and counteroffers until they reach an agreement or until they reach a predetermined deadline.
The players are assumed to be rational and have complete information about their preferences but not about the importance of the other player. The goal of each player is to maximize their utility, which is the measure of their satisfaction or happiness with the outcome of the negotiation. The Rubinstein model seeks an equilibrium, a stable agreement that either player cannot improve upon.

Rubinstein Bargaining game has 3 definitive rules that must be followed through as each stage performed.
* The negotiation begins with an initial offer from one of the parties.
* Initial offer must receive a response in form of either accept, reject, or a counteroffer.
* Bargaing must end with either an agreement is reached or a predetermined timeout deadline is set.

'''Fact:''' The model does not specify a fixed number of stages or a fixed deadline, and the actual number of stages and the length of the negotiation will depend on the specific circumstances of the negotiation.

=Parameters=
The key parameters in the Rubinstein model are the time discount factor and the reservation value.

'''Set of Ordered Pairs:''' The set of ordered pairs is denoted by (s, t), where (s, t) is the discrete representation of time and (s, t) represents a slice of a pie with size 1. Hence, t > 0. Therefore, the pair says, "Player 1 receives s and Player 2 receives 1 - s at time t. The following prerequisites should be met by each player's preferences on (s, t):

'''More Pie or Resource: ''' The best pie is more pie. According to math, if x > y, then (x, t) > (y, t).

'''Time is Money: ''' This indicates that if x > 0 and t2 > t1, then (x, t1) > (x, t2).

'''Continuity: ''' Thus, there are no sudden changes in people's tastes. In terms of mathematics, a preference relation is continuous, In other words, points very near to A will also be preferred to B if we prefer a point A along a preference curve to a point B.

'''Stationary: '''This means that the preference of (x, t) over (y, t + 1) is independent of t.

'''Time Discount Factor:''' The time discount factor represents the degree to which the parties value a settlement reached sooner rather than later. A high-time discount factor means that the parties place a high value on getting an agreement quickly, while a low-time discount factor means they are willing to wait for a more favorable settlement. The time discount factor is often expressed as a decimal between 0 and 1, with higher values indicating a greater preference for settlements reached sooner rather than later. For example, a time discount factor of 0.9 means that the parties place a high value on reaching an agreement quickly, while a time discount factor of 0.1 means that they are willing to wait for a more favorable settlement. So, if (x, t) is equivalent to (y, t + 1) then y needs to be bigger than x to continue one more period with the bargaining and being immaterial to him.

'''Reservation Value:''' The reservation value is the minimum amount of resources that each party is willing to accept in the settlement. If either party's reservation value is not met, they will not agree to the settlement and the negotiation will break down. The reservation value can be thought of as a "fallback" position for each party. If the negotiation breaks down and an agreement is not reached, each party will receive their reservation value rather than nothing. For this reason, the reservation value is often referred to as the "walkaway" value or the "outside option.

=Nash Equilibrium Condition=

[https://www.simulace.info/index.php/Nash_equilibrium Nash Equilibrium] is a solution concept in game theory, which describes a state in which all players in a game are making the best decision they can given the decisions of the other players. The relation between Rubinstein bargaining and Nash equilibrium is that a Nash equilibrium can be reached through the process of Rubinstein bargaining. In other words, if the agents in a negotiation are rational and have complete information, they will eventually reach a Nash equilibrium through the process of making offers and counter-offers.

=Benefits of Rubinstein Bargaining=

The Rubinstein bargaining model has several benefits and positives:

1. It provides a framework for understanding how rational agents will behave in a negotiation and can be utilized to forecast the results of a negotiation.

2. Allows for calculating the Nash Bargaining Solution, a unique and efficient solution for both parties involved in the negotiation.

3. Helps to identify the optimal outcome for both parties involved in the negotiation, which can lead to mutually beneficial agreements.

4. Applicable to various negotiation scenarios, making it a versatile tool for understanding negotiations.

5. Can be used to identify potential sources of conflict and design negotiation strategies to mitigate or avoid them.

6. It is used to understand the role of different factors, such as the outside options and reservation values, in the negotiation process.

7. Researchers have extensively studied and validated it, providing a solid theoretical foundation for its use in real-world negotiations.

=Rubinstein Bargaining and Nash Bargaining Solution=

Rubinstein bargaining model can be used to calculate the Nash bargaining solution, it is not the only way to do so, and the relationship between the two models is somewhat complex. The Nash bargaining solution is a theoretical concept that describes the outcome of a negotiation in which both agents are making their best decisions given the decisions of the other agent. It can be derived from the Nash equilibrium, a state in which all players in a game are making the best decision they can, given the findings of the other players.
The Rubinstein bargaining model is a more specific negotiation model that considers the agents' time discounting and complete information. The Nash bargaining solution, however, does not make any assumptions about the agents' preferences or information and does not consider the surplus's time discounting.

=General Solution=

The solution of the Rubinstein bargaining model is determined by the following formulas:

1. The first formula is for the time-discounted value of the surplus, which is used to calculate the value of an agreement as time passes. The formula is:
V(t) = S / (1 + d*t)
Where:
* V(t) is the time-discounted value of the surplus
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
* t is the time elapsed since the beginning of the negotiation
2. The second formula is for the disagreement point, which represents the value of the best alternative for each agent if they don't reach an agreement. The formula is:
D = (1- d) * S
Where:
* D is the disagreement point
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
3. The third formula is for the Rubinstein bargaining solution, which describes the division of the surplus between the two agents. The formula is:
x = D + (S - D) * (b1 / (b1 + b2))
Where:
* x is the share of the surplus that goes to the first agent
* D is the disagreement point
* S is the total surplus
* b1 and b2 are the bargaining power of the agents, where a high value of b indicates that one agent has more bargaining power than the other.

It's important to notice that this model is a simplified version of the bargaining process, in the real world the negotiation process can be more complicated and factors such as the agents' emotions, trust and communication can affect the outcome.

=Rubinstein Bargaining Game Examples=

A quick and simple example about Rubinstein Barganing game:

'''Game Example 1: '''

A landlord and the tenant bargains over the price of rent. The landlord and the tenant have a common objective of reaching a rental agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

The tenant's outside option is to rent a similar property at a different location, while the landlord's outside option is to keep the property vacant. The potential surplus in this negotiation is the difference between the landlord's profit with a tenant and without a tenant.

The payoffs for each party can be represented by the following formulas:

Tenant: uT(r) = r - r0

Landlord: uL(r) = r - r0 - c

Where r is the agreed rent, r0 is the tenant's reservation price, and c is the landlord's cost of keeping the property vacant.

The Nash Bargaining Solution can be calculated using the following formula:

r = (r0 + c)/2 + (r0 - c)/2 = (r0 + c)

This means that the tenant and the landlord will agree on a rent that is halfway between the tenant's reservation price and the landlord's cost of keeping the property vacant.

For example, if the tenant's reservation price is $1000 and the landlord's cost of keeping the property vacant is $800, the Nash Bargaining Solution is:

r = ($1000 + $800)/2 = $900

This means that the tenant and the landlord will agree on a rent of $900, and both parties will be better off than their outside options. The tenant will be paying less than their reservation price, while the landlord will be earning more than their cost of keeping the property vacant.

'''Game Example 2: '''
This example is about the negotiation process between a buyer and a seller over the price of a car with using Rubinstein Bargaining Solution. The buyer and the seller have a common objective of reaching a sale agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

[[File:car bargaining.jpeg|500px|center]]

The buyer's outside option is to purchase a similar car from a different seller, while the seller's outside option is to keep the car unsold. The potential surplus in this negotiation is the difference between the seller's profit from selling the car and keeping it unsold.

The payoffs for each party can be represented by the following formulas:

Buyer: uB(p) = p - p0

Seller: uS(p) = p - c - p0

Where p is the agreed price, p0 is the buyer's reservation price, and c is the seller's cost of keeping the car unsold.

The Nash Bargaining Solution can be calculated using the following formula:

p = (p0 + c)/2 + (p0 - c)/2 = (p0 + c)

This means that the buyer and the seller will agree on a price that is halfway between the buyer's reservation price and the seller's cost of keeping the car unsold.

For example, if the buyer's reservation price is $15,000 and the seller's cost of keeping the car unsold is $12,000, the Nash Bargaining Solution is:

p = ($15,000 + $12,000)/2 = $13,500

This means that the buyer and the seller will agree on a price of $13,500, and both parties will be better off than their outside options. The buyer will be paying less than their reservation price, while the seller will be earning more than their cost of keeping the car unsold.

=Relevency of Rubinstein Bargaining=

Rubinstein's bargaining is utilized in various fields, including economics, political science, and management. In economics, the model is used to study the market negotiation process and understand the role of information in shaping market outcomes. In political science, the model is used to study the negotiation process in international relations and understand power's role in shaping outcomes. In management, the model is used to study the negotiation process in organizations and to know how different types of administration affect the outcome of negotiations.
In economics, the Rubinstein bargaining theory helps to understand how prices are shaped in markets and how changes in supply and demand affect the price. In international relations, the approach is used to know how countries negotiate treaties and agreements.
In practice, Rubinstein bargaining is also used to study the negotiation process in different sectors, such as labor negotiation, mergers and acquisitions, and international trade.

Rubinstein Bargaining

2023-01-14T10:33:39Z

Kane02:

=Introduction=

In game theory, the Rubinstein bargaining model is a solution to the problem of finding an optimal agreement between two parties who have conflicting interests and asymmetric information. For example lets just say two parties Bob and Alice, engage in a series of alternating offers and counteroffers on a resource that is valuable to both, until they reach an agreement or until they reach a predetermined deadline. How will they behave or what are the necessary steps must be taken by each player? What are the possibile results in the end of the bargaining? In this chapter you will find further details and deepdives about Rubinstein Bargaining concept and solution.

=Problem Definition=

In the Rubinstein bargaining model, two parties usually referred to as "players," are trying to reach an agreement on the division of a pie, where the pie represents a set of resources that are valuable to both parties. The players have conflicting interests and asymmetric information, meaning they have different preferences over how the pie should be divided, and they need complete information about the other player's choices.
The Rubinstein model is a two-stage game.

In the first stage, each player offers the other player how the resource should be split. In the second stage, the other player can accept the offer, reject it, or make a counteroffer. The game continues with the players making alternating offers and counteroffers until they reach an agreement or until they reach a predetermined deadline.
The players are assumed to be rational and have complete information about their preferences but not about the importance of the other player. The goal of each player is to maximize their utility, which is the measure of their satisfaction or happiness with the outcome of the negotiation. The Rubinstein model seeks an equilibrium, a stable agreement that either player cannot improve upon.

Rubinstein Bargaining game has 3 definitive rules that must be followed through as each stage performed.
* The negotiation begins with an initial offer from one of the parties.
* Initial offer must receive a response in form of either accept, reject, or a counteroffer.
* Bargaing must end with either an agreement is reached or a predetermined timeout deadline is set.

'''Fact:''' The model does not specify a fixed number of stages or a fixed deadline, and the actual number of stages and the length of the negotiation will depend on the specific circumstances of the negotiation.

=Parameters=
The key parameters in the Rubinstein model are the time discount factor and the reservation value.

'''Set of Ordered Pairs:''' The set of ordered pairs is denoted by (s, t), where (s, t) is the discrete representation of time and (s, t) represents a slice of a pie with size 1. Hence, t > 0. Therefore, the pair says, "Player 1 receives s and Player 2 receives 1 - s at time t. The following prerequisites should be met by each player's preferences on (s, t):

'''More Pie or Resource: ''' The best pie is more pie. According to math, if x > y, then (x, t) > (y, t).

'''Time is Money: ''' This indicates that if x > 0 and t2 > t1, then (x, t1) > (x, t2).

'''Continuity: ''' Thus, there are no sudden changes in people's tastes. In terms of mathematics, a preference relation is continuous, In other words, points very near to A will also be preferred to B if we prefer a point A along a preference curve to a point B.

'''Stationary: '''This means that the preference of (x, t) over (y, t + 1) is independent of t.

'''Time Discount Factor:''' The time discount factor represents the degree to which the parties value a settlement reached sooner rather than later. A high-time discount factor means that the parties place a high value on getting an agreement quickly, while a low-time discount factor means they are willing to wait for a more favorable settlement. The time discount factor is often expressed as a decimal between 0 and 1, with higher values indicating a greater preference for settlements reached sooner rather than later. For example, a time discount factor of 0.9 means that the parties place a high value on reaching an agreement quickly, while a time discount factor of 0.1 means that they are willing to wait for a more favorable settlement. So, if (x, t) is equivalent to (y, t + 1) then y needs to be bigger than x to continue one more period with the bargaining and being immaterial to him.

'''Reservation Value:''' The reservation value is the minimum amount of resources that each party is willing to accept in the settlement. If either party's reservation value is not met, they will not agree to the settlement and the negotiation will break down. The reservation value can be thought of as a "fallback" position for each party. If the negotiation breaks down and an agreement is not reached, each party will receive their reservation value rather than nothing. For this reason, the reservation value is often referred to as the "walkaway" value or the "outside option.

=Nash Equilibrium Condition=

[https://www.simulace.info/index.php/Nash_equilibrium Nash Equilibrium] is a solution concept in game theory, which describes a state in which all players in a game are making the best decision they can given the decisions of the other players. The relation between Rubinstein bargaining and Nash equilibrium is that a Nash equilibrium can be reached through the process of Rubinstein bargaining. In other words, if the agents in a negotiation are rational and have complete information, they will eventually reach a Nash equilibrium through the process of making offers and counter-offers.

=Benefits of Rubinstein Bargaining=

The Rubinstein bargaining model has several benefits and positives:

1. It provides a framework for understanding how rational agents will behave in a negotiation and can be utilized to forecast the results of a negotiation.

2. Allows for calculating the Nash Bargaining Solution, a unique and efficient solution for both parties involved in the negotiation.

3. Helps to identify the optimal outcome for both parties involved in the negotiation, which can lead to mutually beneficial agreements.

4. Applicable to various negotiation scenarios, making it a versatile tool for understanding negotiations.

5. Can be used to identify potential sources of conflict and design negotiation strategies to mitigate or avoid them.

6. It is used to understand the role of different factors, such as the outside options and reservation values, in the negotiation process.

7. Researchers have extensively studied and validated it, providing a solid theoretical foundation for its use in real-world negotiations.

=General Solution=

The solution of the Rubinstein bargaining model is determined by the following formulas:

1. The first formula is for the time-discounted value of the surplus, which is used to calculate the value of an agreement as time passes. The formula is:
V(t) = S / (1 + d*t)
Where:
* V(t) is the time-discounted value of the surplus
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
* t is the time elapsed since the beginning of the negotiation
2. The second formula is for the disagreement point, which represents the value of the best alternative for each agent if they don't reach an agreement. The formula is:
D = (1- d) * S
Where:
* D is the disagreement point
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
3. The third formula is for the Rubinstein bargaining solution, which describes the division of the surplus between the two agents. The formula is:
x = D + (S - D) * (b1 / (b1 + b2))
Where:
* x is the share of the surplus that goes to the first agent
* D is the disagreement point
* S is the total surplus
* b1 and b2 are the bargaining power of the agents, where a high value of b indicates that one agent has more bargaining power than the other.

It's important to notice that this model is a simplified version of the bargaining process, in the real world the negotiation process can be more complicated and factors such as the agents' emotions, trust and communication can affect the outcome.

=Rubinstein Bargaining Game Examples=

A quick and simple example about Rubinstein Barganing game:

'''Game Example 1: '''

A landlord and the tenant bargains over the price of rent. The landlord and the tenant have a common objective of reaching a rental agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

The tenant's outside option is to rent a similar property at a different location, while the landlord's outside option is to keep the property vacant. The potential surplus in this negotiation is the difference between the landlord's profit with a tenant and without a tenant.

The payoffs for each party can be represented by the following formulas:

Tenant: uT(r) = r - r0

Landlord: uL(r) = r - r0 - c

Where r is the agreed rent, r0 is the tenant's reservation price, and c is the landlord's cost of keeping the property vacant.

The Nash Bargaining Solution can be calculated using the following formula:

r = (r0 + c)/2 + (r0 - c)/2 = (r0 + c)

This means that the tenant and the landlord will agree on a rent that is halfway between the tenant's reservation price and the landlord's cost of keeping the property vacant.

For example, if the tenant's reservation price is $1000 and the landlord's cost of keeping the property vacant is $800, the Nash Bargaining Solution is:

r = ($1000 + $800)/2 = $900

This means that the tenant and the landlord will agree on a rent of $900, and both parties will be better off than their outside options. The tenant will be paying less than their reservation price, while the landlord will be earning more than their cost of keeping the property vacant.

'''Game Example 2: '''
This example is about the negotiation process between a buyer and a seller over the price of a car with using Rubinstein Bargaining Solution. The buyer and the seller have a common objective of reaching a sale agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

[[File:car bargaining.jpeg|500px|center]]

The buyer's outside option is to purchase a similar car from a different seller, while the seller's outside option is to keep the car unsold. The potential surplus in this negotiation is the difference between the seller's profit from selling the car and keeping it unsold.

The payoffs for each party can be represented by the following formulas:

Buyer: uB(p) = p - p0

Seller: uS(p) = p - c - p0

Where p is the agreed price, p0 is the buyer's reservation price, and c is the seller's cost of keeping the car unsold.

The Nash Bargaining Solution can be calculated using the following formula:

p = (p0 + c)/2 + (p0 - c)/2 = (p0 + c)

This means that the buyer and the seller will agree on a price that is halfway between the buyer's reservation price and the seller's cost of keeping the car unsold.

For example, if the buyer's reservation price is $15,000 and the seller's cost of keeping the car unsold is $12,000, the Nash Bargaining Solution is:

p = ($15,000 + $12,000)/2 = $13,500

This means that the buyer and the seller will agree on a price of $13,500, and both parties will be better off than their outside options. The buyer will be paying less than their reservation price, while the seller will be earning more than their cost of keeping the car unsold.

=Relevency of Rubinstein Bargaining=

Rubinstein's bargaining is utilized in various fields, including economics, political science, and management. In economics, the model is used to study the market negotiation process and understand the role of information in shaping market outcomes. In political science, the model is used to study the negotiation process in international relations and understand power's role in shaping outcomes. In management, the model is used to study the negotiation process in organizations and to know how different types of administration affect the outcome of negotiations.
In economics, the Rubinstein bargaining theory helps to understand how prices are shaped in markets and how changes in supply and demand affect the price. In international relations, the approach is used to know how countries negotiate treaties and agreements.
In practice, Rubinstein bargaining is also used to study the negotiation process in different sectors, such as labor negotiation, mergers and acquisitions, and international trade.

Rubinstein Bargaining

2023-01-14T10:33:14Z

Kane02:

=Introduction=

In game theory, the Rubinstein bargaining model is a solution to the problem of finding an optimal agreement between two parties who have conflicting interests and asymmetric information. For example lets just say two parties Bob and Alice, engage in a series of alternating offers and counteroffers on a resource that is valuable to both, until they reach an agreement or until they reach a predetermined deadline. How will they behave or what are the necessary steps must be taken by each player? What are the possibile results in the end of the bargaining? In this chapter you will find further details and deepdives about Rubinstein Bargaining concept and solution.

=Problem Definition=

In the Rubinstein bargaining model, two parties usually referred to as "players," are trying to reach an agreement on the division of a pie, where the pie represents a set of resources that are valuable to both parties. The players have conflicting interests and asymmetric information, meaning they have different preferences over how the pie should be divided, and they need complete information about the other player's choices.
The Rubinstein model is a two-stage game.

In the first stage, each player offers the other player how the resource should be split. In the second stage, the other player can accept the offer, reject it, or make a counteroffer. The game continues with the players making alternating offers and counteroffers until they reach an agreement or until they reach a predetermined deadline.
The players are assumed to be rational and have complete information about their preferences but not about the importance of the other player. The goal of each player is to maximize their utility, which is the measure of their satisfaction or happiness with the outcome of the negotiation. The Rubinstein model seeks an equilibrium, a stable agreement that either player cannot improve upon.

Rubinstein Bargaining game has 3 definitive rules that must be followed through as each stage performed.
* The negotiation begins with an initial offer from one of the parties.
* Initial offer must receive a response in form of either accept, reject, or a counteroffer.
* Bargaing must end with either an agreement is reached or a predetermined timeout deadline is set.

'''Fact:''' The model does not specify a fixed number of stages or a fixed deadline, and the actual number of stages and the length of the negotiation will depend on the specific circumstances of the negotiation.

=Parameters=
The key parameters in the Rubinstein model are the time discount factor and the reservation value.

'''Set of Ordered Pairs:''' The set of ordered pairs is denoted by (s, t), where (s, t) is the discrete representation of time and (s, t) represents a slice of a pie with size 1. Hence, t > 0. Therefore, the pair says, "Player 1 receives s and Player 2 receives 1 - s at time t. The following prerequisites should be met by each player's preferences on (s, t):

'''More Pie or Resource: ''' The best pie is more pie. According to math, if x > y, then (x, t) > (y, t).

'''Time is Money: ''' This indicates that if x > 0 and t2 > t1, then (x, t1) > (x, t2).

'''Continuity: ''' Thus, there are no sudden changes in people's tastes. In terms of mathematics, a preference relation is continuous, In other words, points very near to A will also be preferred to B if we prefer a point A along a preference curve to a point B.

'''Stationary: '''This means that the preference of (x, t) over (y, t + 1) is independent of t.

'''Time Discount Factor:''' The time discount factor represents the degree to which the parties value a settlement reached sooner rather than later. A high-time discount factor means that the parties place a high value on getting an agreement quickly, while a low-time discount factor means they are willing to wait for a more favorable settlement. The time discount factor is often expressed as a decimal between 0 and 1, with higher values indicating a greater preference for settlements reached sooner rather than later. For example, a time discount factor of 0.9 means that the parties place a high value on reaching an agreement quickly, while a time discount factor of 0.1 means that they are willing to wait for a more favorable settlement. So, if (x, t) is equivalent to (y, t + 1) then y needs to be bigger than x to continue one more period with the bargaining and being immaterial to him.

'''Reservation Value:''' The reservation value is the minimum amount of resources that each party is willing to accept in the settlement. If either party's reservation value is not met, they will not agree to the settlement and the negotiation will break down. The reservation value can be thought of as a "fallback" position for each party. If the negotiation breaks down and an agreement is not reached, each party will receive their reservation value rather than nothing. For this reason, the reservation value is often referred to as the "walkaway" value or the "outside option.

=Nash Equilibrium Condition=

[https://www.simulace.info/index.php/Nash_equilibrium Nash Equilibrium] is a solution concept in game theory, which describes a state in which all players in a game are making the best decision they can given the decisions of the other players. The relation between Rubinstein bargaining and Nash equilibrium is that a Nash equilibrium can be reached through the process of Rubinstein bargaining. In other words, if the agents in a negotiation are rational and have complete information, they will eventually reach a Nash equilibrium through the process of making offers and counter-offers.

=Benefits of Rubinstein Bargaining=

The Rubinstein bargaining model has several benefits and positives:

1. It provides a framework for understanding how rational agents will behave in a negotiation and can be utilized to forecast the results of a negotiation.
2. Allows for calculating the Nash Bargaining Solution, a unique and efficient solution for both parties involved in the negotiation.
3. Helps to identify the optimal outcome for both parties involved in the negotiation, which can lead to mutually beneficial agreements.
4. Applicable to various negotiation scenarios, making it a versatile tool for understanding negotiations.
5. Can be used to identify potential sources of conflict and design negotiation strategies to mitigate or avoid them.
6. It is used to understand the role of different factors, such as the outside options and reservation values, in the negotiation process.
7. Researchers have extensively studied and validated it, providing a solid theoretical foundation for its use in real-world negotiations.

=General Solution=

The solution of the Rubinstein bargaining model is determined by the following formulas:

1. The first formula is for the time-discounted value of the surplus, which is used to calculate the value of an agreement as time passes. The formula is:
V(t) = S / (1 + d*t)
Where:
* V(t) is the time-discounted value of the surplus
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
* t is the time elapsed since the beginning of the negotiation
2. The second formula is for the disagreement point, which represents the value of the best alternative for each agent if they don't reach an agreement. The formula is:
D = (1- d) * S
Where:
* D is the disagreement point
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
3. The third formula is for the Rubinstein bargaining solution, which describes the division of the surplus between the two agents. The formula is:
x = D + (S - D) * (b1 / (b1 + b2))
Where:
* x is the share of the surplus that goes to the first agent
* D is the disagreement point
* S is the total surplus
* b1 and b2 are the bargaining power of the agents, where a high value of b indicates that one agent has more bargaining power than the other.

It's important to notice that this model is a simplified version of the bargaining process, in the real world the negotiation process can be more complicated and factors such as the agents' emotions, trust and communication can affect the outcome.

=Rubinstein Bargaining Game Examples=

A quick and simple example about Rubinstein Barganing game:

'''Game Example 1: '''

A landlord and the tenant bargains over the price of rent. The landlord and the tenant have a common objective of reaching a rental agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

The tenant's outside option is to rent a similar property at a different location, while the landlord's outside option is to keep the property vacant. The potential surplus in this negotiation is the difference between the landlord's profit with a tenant and without a tenant.

The payoffs for each party can be represented by the following formulas:

Tenant: uT(r) = r - r0

Landlord: uL(r) = r - r0 - c

Where r is the agreed rent, r0 is the tenant's reservation price, and c is the landlord's cost of keeping the property vacant.

The Nash Bargaining Solution can be calculated using the following formula:

r = (r0 + c)/2 + (r0 - c)/2 = (r0 + c)

This means that the tenant and the landlord will agree on a rent that is halfway between the tenant's reservation price and the landlord's cost of keeping the property vacant.

For example, if the tenant's reservation price is $1000 and the landlord's cost of keeping the property vacant is $800, the Nash Bargaining Solution is:

r = ($1000 + $800)/2 = $900

This means that the tenant and the landlord will agree on a rent of $900, and both parties will be better off than their outside options. The tenant will be paying less than their reservation price, while the landlord will be earning more than their cost of keeping the property vacant.

'''Game Example 2: '''
This example is about the negotiation process between a buyer and a seller over the price of a car with using Rubinstein Bargaining Solution. The buyer and the seller have a common objective of reaching a sale agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

[[File:car bargaining.jpeg|500px|center]]

The buyer's outside option is to purchase a similar car from a different seller, while the seller's outside option is to keep the car unsold. The potential surplus in this negotiation is the difference between the seller's profit from selling the car and keeping it unsold.

The payoffs for each party can be represented by the following formulas:

Buyer: uB(p) = p - p0

Seller: uS(p) = p - c - p0

Where p is the agreed price, p0 is the buyer's reservation price, and c is the seller's cost of keeping the car unsold.

The Nash Bargaining Solution can be calculated using the following formula:

p = (p0 + c)/2 + (p0 - c)/2 = (p0 + c)

This means that the buyer and the seller will agree on a price that is halfway between the buyer's reservation price and the seller's cost of keeping the car unsold.

For example, if the buyer's reservation price is $15,000 and the seller's cost of keeping the car unsold is $12,000, the Nash Bargaining Solution is:

p = ($15,000 + $12,000)/2 = $13,500

This means that the buyer and the seller will agree on a price of $13,500, and both parties will be better off than their outside options. The buyer will be paying less than their reservation price, while the seller will be earning more than their cost of keeping the car unsold.

=Relevency of Rubinstein Bargaining=

Rubinstein's bargaining is utilized in various fields, including economics, political science, and management. In economics, the model is used to study the market negotiation process and understand the role of information in shaping market outcomes. In political science, the model is used to study the negotiation process in international relations and understand power's role in shaping outcomes. In management, the model is used to study the negotiation process in organizations and to know how different types of administration affect the outcome of negotiations.
In economics, the Rubinstein bargaining theory helps to understand how prices are shaped in markets and how changes in supply and demand affect the price. In international relations, the approach is used to know how countries negotiate treaties and agreements.
In practice, Rubinstein bargaining is also used to study the negotiation process in different sectors, such as labor negotiation, mergers and acquisitions, and international trade.

File:Car bargaining.jpeg

2023-01-14T10:31:45Z

Kane02:

Rubinstein Bargaining

2023-01-14T10:31:06Z

Kane02:

=Introduction=

In game theory, the Rubinstein bargaining model is a solution to the problem of finding an optimal agreement between two parties who have conflicting interests and asymmetric information. For example lets just say two parties Bob and Alice, engage in a series of alternating offers and counteroffers on a resource that is valuable to both, until they reach an agreement or until they reach a predetermined deadline. How will they behave or what are the necessary steps must be taken by each player? What are the possibile results in the end of the bargaining? In this chapter you will find further details and deepdives about Rubinstein Bargaining concept and solution.

=Problem Definition=

In the Rubinstein bargaining model, two parties usually referred to as "players," are trying to reach an agreement on the division of a pie, where the pie represents a set of resources that are valuable to both parties. The players have conflicting interests and asymmetric information, meaning they have different preferences over how the pie should be divided, and they need complete information about the other player's choices.
The Rubinstein model is a two-stage game.

In the first stage, each player offers the other player how the resource should be split. In the second stage, the other player can accept the offer, reject it, or make a counteroffer. The game continues with the players making alternating offers and counteroffers until they reach an agreement or until they reach a predetermined deadline.
The players are assumed to be rational and have complete information about their preferences but not about the importance of the other player. The goal of each player is to maximize their utility, which is the measure of their satisfaction or happiness with the outcome of the negotiation. The Rubinstein model seeks an equilibrium, a stable agreement that either player cannot improve upon.

Rubinstein Bargaining game has 3 definitive rules that must be followed through as each stage performed.
* The negotiation begins with an initial offer from one of the parties.
* Initial offer must receive a response in form of either accept, reject, or a counteroffer.
* Bargaing must end with either an agreement is reached or a predetermined timeout deadline is set.

'''Fact:''' The model does not specify a fixed number of stages or a fixed deadline, and the actual number of stages and the length of the negotiation will depend on the specific circumstances of the negotiation.

=Parameters=
The key parameters in the Rubinstein model are the time discount factor and the reservation value.

'''Set of Ordered Pairs:''' The set of ordered pairs is denoted by (s, t), where (s, t) is the discrete representation of time and (s, t) represents a slice of a pie with size 1. Hence, t > 0. Therefore, the pair says, "Player 1 receives s and Player 2 receives 1 - s at time t. The following prerequisites should be met by each player's preferences on (s, t):

'''More Pie or Resource: ''' The best pie is more pie. According to math, if x > y, then (x, t) > (y, t).

'''Time is Money: ''' This indicates that if x > 0 and t2 > t1, then (x, t1) > (x, t2).

'''Continuity: ''' Thus, there are no sudden changes in people's tastes. In terms of mathematics, a preference relation is continuous, In other words, points very near to A will also be preferred to B if we prefer a point A along a preference curve to a point B.

'''Stationary: '''This means that the preference of (x, t) over (y, t + 1) is independent of t.

'''Time Discount Factor:''' The time discount factor represents the degree to which the parties value a settlement reached sooner rather than later. A high-time discount factor means that the parties place a high value on getting an agreement quickly, while a low-time discount factor means they are willing to wait for a more favorable settlement. The time discount factor is often expressed as a decimal between 0 and 1, with higher values indicating a greater preference for settlements reached sooner rather than later. For example, a time discount factor of 0.9 means that the parties place a high value on reaching an agreement quickly, while a time discount factor of 0.1 means that they are willing to wait for a more favorable settlement. So, if (x, t) is equivalent to (y, t + 1) then y needs to be bigger than x to continue one more period with the bargaining and being immaterial to him.

'''Reservation Value:''' The reservation value is the minimum amount of resources that each party is willing to accept in the settlement. If either party's reservation value is not met, they will not agree to the settlement and the negotiation will break down. The reservation value can be thought of as a "fallback" position for each party. If the negotiation breaks down and an agreement is not reached, each party will receive their reservation value rather than nothing. For this reason, the reservation value is often referred to as the "walkaway" value or the "outside option.

=Nash Equilibrium Condition=

[https://www.simulace.info/index.php/Nash_equilibrium Nash Equilibrium] is a solution concept in game theory, which describes a state in which all players in a game are making the best decision they can given the decisions of the other players. The relation between Rubinstein bargaining and Nash equilibrium is that a Nash equilibrium can be reached through the process of Rubinstein bargaining. In other words, if the agents in a negotiation are rational and have complete information, they will eventually reach a Nash equilibrium through the process of making offers and counter-offers.

=Benefits of Rubinstein Bargaining=

The Rubinstein bargaining model has several benefits and positives:
1. It provides a framework for understanding how rational agents will behave in a negotiation and can be utilized to forecast the results of a negotiation.
2. Allows for calculating the Nash Bargaining Solution, a unique and efficient solution for both parties involved in the negotiation.
3. Helps to identify the optimal outcome for both parties involved in the negotiation, which can lead to mutually beneficial agreements.
4. Applicable to various negotiation scenarios, making it a versatile tool for understanding negotiations.
5. Can be used to identify potential sources of conflict and design negotiation strategies to mitigate or avoid them.
6. It is used to understand the role of different factors, such as the outside options and reservation values, in the negotiation process.
7. Researchers have extensively studied and validated it, providing a solid theoretical foundation for its use in real-world negotiations.

=General Solution=

The solution of the Rubinstein bargaining model is determined by the following formulas:

1. The first formula is for the time-discounted value of the surplus, which is used to calculate the value of an agreement as time passes. The formula is:
V(t) = S / (1 + d*t)
Where:
* V(t) is the time-discounted value of the surplus
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
* t is the time elapsed since the beginning of the negotiation
2. The second formula is for the disagreement point, which represents the value of the best alternative for each agent if they don't reach an agreement. The formula is:
D = (1- d) * S
Where:
* D is the disagreement point
* S is the total surplus
* d is the discount factor, represents the agents' time preferences.
3. The third formula is for the Rubinstein bargaining solution, which describes the division of the surplus between the two agents. The formula is:
x = D + (S - D) * (b1 / (b1 + b2))
Where:
* x is the share of the surplus that goes to the first agent
* D is the disagreement point
* S is the total surplus
* b1 and b2 are the bargaining power of the agents, where a high value of b indicates that one agent has more bargaining power than the other.

It's important to notice that this model is a simplified version of the bargaining process, in the real world the negotiation process can be more complicated and factors such as the agents' emotions, trust and communication can affect the outcome.

=Rubinstein Bargaining Game Examples=

A quick and simple example about Rubinstein Barganing game:

'''Game Example 1: '''

A landlord and the tenant bargains over the price of rent. The landlord and the tenant have a common objective of reaching a rental agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

The tenant's outside option is to rent a similar property at a different location, while the landlord's outside option is to keep the property vacant. The potential surplus in this negotiation is the difference between the landlord's profit with a tenant and without a tenant.

The payoffs for each party can be represented by the following formulas:

Tenant: uT(r) = r - r0

Landlord: uL(r) = r - r0 - c

Where r is the agreed rent, r0 is the tenant's reservation price, and c is the landlord's cost of keeping the property vacant.

The Nash Bargaining Solution can be calculated using the following formula:

r = (r0 + c)/2 + (r0 - c)/2 = (r0 + c)

This means that the tenant and the landlord will agree on a rent that is halfway between the tenant's reservation price and the landlord's cost of keeping the property vacant.

For example, if the tenant's reservation price is $1000 and the landlord's cost of keeping the property vacant is $800, the Nash Bargaining Solution is:

r = ($1000 + $800)/2 = $900

This means that the tenant and the landlord will agree on a rent of $900, and both parties will be better off than their outside options. The tenant will be paying less than their reservation price, while the landlord will be earning more than their cost of keeping the property vacant.

'''Game Example 2: '''
This example is about the negotiation process between a buyer and a seller over the price of a car with using Rubinstein Bargaining Solution. The buyer and the seller have a common objective of reaching a sale agreement that is mutually beneficial. Both sides have complete information about the issue at hand and their own preferences, and are rational and will choose strategies that maximize their expected payoffs.

[[File:car bargaining.jpeg|500px|center]]

The buyer's outside option is to purchase a similar car from a different seller, while the seller's outside option is to keep the car unsold. The potential surplus in this negotiation is the difference between the seller's profit from selling the car and keeping it unsold.

The payoffs for each party can be represented by the following formulas:

Buyer: uB(p) = p - p0

Seller: uS(p) = p - c - p0

Where p is the agreed price, p0 is the buyer's reservation price, and c is the seller's cost of keeping the car unsold.

The Nash Bargaining Solution can be calculated using the following formula:

p = (p0 + c)/2 + (p0 - c)/2 = (p0 + c)

This means that the buyer and the seller will agree on a price that is halfway between the buyer's reservation price and the seller's cost of keeping the car unsold.

For example, if the buyer's reservation price is $15,000 and the seller's cost of keeping the car unsold is $12,000, the Nash Bargaining Solution is:

p = ($15,000 + $12,000)/2 = $13,500

This means that the buyer and the seller will agree on a price of $13,500, and both parties will be better off than their outside options. The buyer will be paying less than their reservation price, while the seller will be earning more than their cost of keeping the car unsold.

=Relevency of Rubinstein Bargaining=

Rubinstein's bargaining is utilized in various fields, including economics, political science, and management. In economics, the model is used to study the market negotiation process and understand the role of information in shaping market outcomes. In political science, the model is used to study the negotiation process in international relations and understand power's role in shaping outcomes. In management, the model is used to study the negotiation process in organizations and to know how different types of administration affect the outcome of negotiations.
In economics, the Rubinstein bargaining theory helps to understand how prices are shaped in markets and how changes in supply and demand affect the price. In international relations, the approach is used to know how countries negotiate treaties and agreements.
In practice, Rubinstein bargaining is also used to study the negotiation process in different sectors, such as labor negotiation, mergers and acquisitions, and international trade.

Rubinstein Bargaining

2023-01-13T21:51:58Z

Kane02:

Rubinstein Bargaining

2023-01-08T16:34:13Z

Kane02:

Rubinstein Bargaining

2023-01-08T16:33:35Z

Kane02:

Rubinstein Bargaining

2023-01-07T17:39:06Z

Kane02:

Rubinstein Bargaining

2023-01-07T16:14:07Z

Kane02:

Rubinstein Bargaining

2023-01-06T09:35:38Z

Kane02: Created page with " =Introduction= In game theory, the Rubinstein bargaining model is a solution to the problem of finding an optimal agreement between two parties who have conflicting interest..."

Course materials

2023-01-06T08:16:08Z

Kane02:

Please, read the article [[How to write a term paper]] for the hints for writing your semestral paper. '''Make sure''' that your assignment is really writing a course material, not a Wikipedia article! Wikipedia article is to be submitted always and exclusively directly into Wikipedia!

==Materials online==
*[[Monte Carlo method]]
**[[Pseudorandom number generators]]
**[[Randomness tests]]
**[[Probability distributions]]
**[[Variance reduction]]
**[[Monte Carlo method in simulations]]
**[[Interpretation of MC simulation results (Stochastic methods)]]
*[[Discrete event simulation]]
**[[Queueing theory]]
**[[Simulation in Quality management]]
*[[Game theory]]
**[[Nash equilibrium]]
***[[Mixed strategy]]
**[[One-shot games]]
***[[Normal form]]
***[[Prisoner's dilemma]]
***[[The Chicken Game]]
**[[Repeated games]]
**[[Multistage Games]]
***[[Extensive form]]
**[[Multiplayer games]]
***[[Auctions]]
****[[Vickrey's auction]]
***[[N-player prisoner's dilemma]]
***[[Multiplayer cooperative games]]
***[[Rubinstein Bargaining]]
*[[Multi-agent systems]]
**[[Agents]]
***[[Agent reasoning]]
****[[Markov decision process]]
**[[Agent Environments]]
*[[System Dynamics]]
**[[Causal loop diagram]]
**[[Stock and flow diagram]]
**[[Leverage point]]
**[[System Archetypes]]
***[[Tragedy of the commons]]
***[[Growth and Underinvestment]]
***[[Limits to Growth]]
***[[Shifting the Burden]]
***[[Fixes That Fail]]
***[[Drifting Goals]]
*[[Serious Gaming]]
**[[Virtual reality and serious games]]
==Required reading==
* Šalamon, T. (2011). [http://www.designofagentbasedmodels.info ''Design of Agent-Based Models : Developing Computer Simulations for a Better Understanding of Social Processes'']. Řepín, Czech Republic: Bruckner Publishing

==Recommended reading==
* Colman, A. M. (1982). ''Game theory and experimental games : the study of strategic interaction''. Oxford, UK: Pergamon
* Sterman, J. (2000). ''Business dynamics : systems thinking and modeling for a complex world''. Boston, Ma.: Irwin/McGraw-Hill
* Wooldridge, M. J. (2002). ''An introduction to multiagent systems''. Chichester, UK: John Wiley & Sons
* Polak, B. (2007) ''Game Theory'' In: Yale University: Open Yale Courses, [http://oyc.yale.edu/economics/econ-159 http://oyc.yale.edu/]

Assignments WS 2022/2023

2022-12-18T13:10:28Z

Kane02:

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Please, put here your assignments. Do not forget to sign them. You can use <nowiki>~~~~</nowiki> (four tildas) for an automatic signature. Use Show preview in order to check the result before your final sumbition.
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Please, strive to formulate your assignment carefully. We expect an adequate effort to formulate the assignment as it is your semestral paper. Do not forget that your main goal is a research paper. It means your simulation model must generate the results that are specific, measurable and verifiable. Think twice how you will develop your model, which entities you will use, draw a model diagram, consider what you will measure. No sooner than when you have a good idea about the model, submit your assignment. And of course, read [[How to deal with the simulation assignment|How to deal with the simulation assignment]].
</div>
}}

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Topics on gambling, cards, etc. are not welcome.
</div>
}}

{{Ambox
| type = content
| text = <div>
In order to avoid possible confusion, please, check if you have added '''approved''' in bold somewhere in our comment under your submission. If there is no '''approved''', it means the assignment was not approved yet.
</div>
}}

== Effect of leniency programs on cartel rates by [[User:Baumareb|Baumareb]] ([[User talk:Baumareb|talk]]) 11:18, 7 December 2022 (CET) ==

''' Simulation '''

The leniency program of the European Commission offers the companies involved in a cartel either complete or partial immunity from fines if they self-report and hand over evidence. It was introduced in 1996, following the surge in amnesty applications in the wake of the 1993 revision of the Corporate Leniency Program of the US Department of Justice’s Antitrust Division. Reports from various implemented leniency programs showed that such programs led to numerous applications. However, despite the clear increase in leniency applications, the question poses itself as to whether the programs were also successful in a sense that the actual cartel rate in those countries declined.
The simulation will be based on a study of Harrington and Chang from 2015, in which they concluded the following:

• The actual cartel rate decreases in case that the leniency program does not affect the non-leniency enforcement

• But: if the non-leniency enforcement is affected because resources are shifted to the prosecution of leniency application cases, there might be two possibilities, the cartel rate might increase.

This simulation focuses on the latter case. Assuming endogenized non-leniency enforcement, the introduction of a leniency program might have a differential impact on different industries. If a leniency program is introduced, the cartels that are about to collapse will seek to self-report. This in turn shifts resources from exposing active cartels to prosecuting cartels that are already collapsing. This creates more work for the authorities, who, instead of focusing on active cartels may now focus on dying cartels. This crowding-out effect coming about with the introduction of a leniency program shall be simulated in this project.

''' Goal '''

The simulation will have the following objectives:

* Illustrate the change in cartel rates and the change in the average life expectancy of a cartel triggered by the introduction of a leniency program in case of endogenized non-leniency enforcement for industries with unstable cartels (e.g. industries with a high number of competitors, or demand with more price elasticity) and for industries with stable cartels (e.g. industries with less competitors and demand with less price elasticity).
* Illustrate how many resources may be shifted from non-leniency enforcement to prosecuting leniency application cases without it having an undesired effect on the actual cartel rate.

''' Practical relevance '''

The simulation may be used by law enforcement officials to evaluate whether a leniency program leads to the desired effect (i.e. the decrease in the cartel rate) or not. Also, it can help for deciding whether the non-leniency enforcement needs to be strengthened to prevent the crowding-out effect.

''' Method '''

The described scenario is a multi-agent simulation in which the agents are pursuing a utility-based approach. Thus, the simulation will be done with NetLogo.
The following features will be included into the simulation:

- For both industries with stable and industries with unstable cartels:

* Number of active cartels (dying after reaching avg. life expectancy)
* Number of competitors
* Average life expectancy of a cartel
* “Birth” of new cartels

- For leniency/non-leniency enforcement:
* Resources and their assignment to either leniency or non-leniency enforcement
* Capacity of taking down an active cartel
* Capacity of taking down a cartel based on leniency applications

The simulation will be based on the 2015 research from Harrington and Chang as well as on publicly accessible data from the European Commission regarding antitrust cases from 1964 until today.

''' Sources '''
* Harrington Jr, J. E., & Chang, M. H. (2015). When can we expect a corporate leniency program to result in fewer cartels?. The Journal of Law and Economics, 58(2), 417-449.
* Ordóñez‐De‐Haro, J. M., Borrell, J. R., & Jiménez, J. L. (2018). The European commission's fight against cartels (1962–2014): A retrospective and forensic analysis. JCMS: Journal of Common Market Studies, 56(5), 1087-1107.

[[User:Baumareb|Baumareb]] ([[User talk:Baumareb|talk]]) 11:18, 7 December 2022 (CET) Rebecca Baumann (baur00)

: This isn't an easy topic. Be careful about available data. '''Approved''' [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 01:46, 15 December 2022 (CET)

== The prediction of divorce rate in Czech Republic for the following 50 years ==

''' The goal of the simulation '''

Divorce in the Czech republic must always contain at least one hearing in front of the court. Legally, there are many more parties involved, such as a notary, who must verify the signatures on all the important documents and many times, divorce lawyers are also necessary. To be able to satisfy the needs of the public, all the involved parties must have an idea about how many married couples are likely to get divorced in the years to come. This simulation will help prepare the courts, notaries and lawyers by making a prediction on the amount of divorces in the next 50 years. This will also help law students choose the field of law that they will specialize in by answering the question whether divorce lawyers will be necessary in the future or not.

''' Method '''

Vensim will be used for this simulation. The used data will come from the Czech Statistical Office and possibly other sources (Refer to [1] and [2]), such as published studies on the most common reasons for divorce. When possible, the data about each reason of divorce will be also found and the simulation model will contain this data.

== Edit: additional details ==

''' What all parameters will the simulation work with and how?'''

1. Number of marriages – the more marriages, the more divorces

a/ Number of people in the age 25 to 34 (i.e., the most common age to get married) – the more there is of these people, the more marriages there will be

b/ Number of divorced people in the age 40 to 49 (i.e., the most common age to get re-married after a divorce) – the more there is of these people, the more marriages there will be, however not as much as the number above

2. Micro causes of divorces = Top 10 causes of divorce as researched by the Czech Statistical Office, published yearly – the more common are these causes (alcoholism, infidelity etc), the more divorces there will be

a/ Ill-considered marriage

b/ Alcoholism

c/ Infidelity

d/ Lack of interest in the family (incl. abandon. of living together)

e/ Ill-treatment, criminal conviction

f/ Different characters, views and interests

g/ Health reasons

h/ Sexual discord

i/ Other causes

j/ Cause not given

3. Number of people in the age 40 to 49 – the more there is of these people, the more divorces there will be (it is the most common age to get divorced)

4. Macro causes of divorces

a/ Economic independence of women = the more economically independent women are, the more likely they are to divorce in case of an unhappy marriage – this will be evaluated through a comparison of data of average income of men vs. women

b/ Being religious – divorce is far less common for religious people.

''' What data source will be used for deriving the equations?'''

Based on my current research of data sources, the Czech Statistical Office has the all the data necessary for this paper.

[1] Scott, S. B., Rhoades, G. K., Stanley, S. M., Allen, E. S., & Markman, H. J. (2013). Reasons for Divorce and Recollections of Premarital Intervention: Implications for Improving Relationship Education. Couple & family psychology, 2(2), 131–145. https://doi.org/10.1037/a0032025

[2] Hawkins, Alan & Willoughby, Brian & Doherty, William. (2012). Reasons for Divorce and Openness to Marital Reconciliation. Journal of Divorce & Remarriage. 53. 453-463. 10.1080/10502556.2012.682898.

: Sounds interesting, but I miss more detail about the simulation. What all parameters will the simulation work with and how? What data source will be used for deriving the equations? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 11:03, 15 December 2022 (CET)
:: ''' Approved'''. Just make sure that the equtions, reasons for divorce and their impact on divorce rate are properly quantified.[[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 07:23, 17 December 2022 (CET)

==Crop Yield Forecasting==

''' Simulation '''

Crop growth and development simulations and yield forecasting will be performed using variables such as crop type, planting date, soil type, soil texture, and climate data (temperature, rainfall, etc.).

'''Problem definition'''

Arable land is increasingly limited, while the world's population has steadily been increasing over the years. In order to meet rapidly rising demand, production must be increased while natural resources must be protected. New agricultural research is needed to provide information on how to achieve sustainable agriculture in the face of global climate variability. Predicting crop yield under different conditions, such as different irrigation regimes, planting dates, and crop management practices, has become critical for farmers and other stakeholders who use these predictions to make more informed decisions about how to allocate resources, such as labor, equipment, and inputs, to maximize yield and productivity.

'''Method'''

Crop yield simulation tools include AquaCrop, DSSAT, and CropSyst. These tools use mathematical models to simulate crop growth and development based on input data like weather, soil type, and management practices. These tools use this data to estimate the crop's potential yield, as well as other important factors like water use and crop evapotranspiration. For this assignment I will be using AquaCrop which is a crop water productivity model developed by the United Nations Food and Agriculture Organization (FAO). It is used to simulate crop growth and yield under various environmental and management conditions. AquaCrop simulates crop growth and development, and estimates yield based on soil conditions, climate, irrigation, and management practices. The application gives access to various FAO databases with all the necessary data needed to perform a comprehensive simulation of the crop yield.

'''Citations'''

* Y. Lu, C. Wei, M. F. McCabe, and J. Sheffield, “Multi-variable assimilation into a modified AquaCrop model for improved maize simulation without management or crop phenology information,” Agricultural Water Management, vol. 266, p. 107576, May 2022, doi: 10.1016/j.agwat.2022.107576.
* P. N. Kephe, K. K. Ayisi, and B. M. Petja, “Challenges and opportunities in crop simulation modelling under seasonal and projected climate change scenarios for crop production in South Africa,” Agriculture & Food Security, vol. 10, no. 1, p. 10, Apr. 2021, doi: 10.1186/s40066-020-00283-5.
* N. T. Olivera, O. B. Manrique, Y. G. Masjuan, and A. M. G. Alega, “Evaluation of AquaCrop model in crop dry bean growth simulation,” Revista Ciencias Técnicas Agropecuarias, vol. 25, no. 3, pp. 23–30, Accessed: Dec. 10, 2022. [Online]. Available: https://www.redalyc.org/journal/932/93246970003/html/
* N. Pirmoradian, Z. Saadati, M. Rezaei, and M. R. Khaledian, “Simulating water productivity of paddy rice under irrigation regimes using AquaCrop model in humid and semiarid regions of Iran,” Appl Water Sci, vol. 10, no. 7, p. 161, Jun. 2020, doi: 10.1007/s13201-020-01249-5.

[[User:Pierreatekwana|Pierreatekwana]] ([[User talk:Pierreatekwana|talk]]) 15:06, 15 December 2022 (CET)

: Topic souds interesting, but the proposed simulation tool has to be one of the ones we have used in our class ( as specified in How to deal with the simulation assignment:
One of your key course requirements is a submission of simulation. You choose your topic yourself, the same as a method and a tool that you will use. It could be any of the development environments we have used (Excel, Simprocess, Netlogo, or Vensim).) [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 07:05, 17 December 2022 (CET)

== Electricity Spot Market Simulation by [[User:Ceta|Ceta]] ([[User talk:Ceta|talk]]) 01:13, 16 December 2022 (CET) ==

== IDEA 1 ==

'''Problem definition'''

Anthony is as a portfolio manager in the power company Goodpower. Goodpower has a portfolio of power plants. Goodpower is a market participant in a liberated market structure. The power generation can be sold either in spot market with volatile prices, or it can be sold with a yearly fixed price on over the counter (OTC). Goodpower assigned Anthony responsible for optimization of power generation revenue. Now Anthony needs to decide on how much generation to risk in the volatile spot market and how much to risk with the fixed price. After contacting the power brokers in OTC market, he was offered the following deals:

1. A baseload deal with a fixed price.

2. An off-peak hours deal with a fixed price.

3. A peak hours deal with a fixed price.

'''Goal'''

Simulation that can be used as a decision support tool when managing a power portfolio.

'''Method'''

Monte Carlo simulation in Excel environment will be created. The historical spot prices will be used to determine fixed deal prices. The historical generation values will be used to determine generation scenarios (wet season - high.generation, average generation, dry season – low generation). The volatility of spot market prices will be based on again historical spot prices. The simulation of 1 year = 8760 hours will be generated. Since, the stability spot market prices in winter are dependent on natural gas shortages, these shortage scenarios will be added to the simulation.

'''Model parameters'''

• Generation scenarios:

- Wet season – high generation (MWh)

- Average season - average generation (MWh)

- Dry season – low generation (MWh)

• Market data:

- Volatile spot market prices (USD/MWh)

- Fixed deal prices will be based on past year spot market prices (While OTC market prices can’t be publicly viewed)

''' Data '''

- EXIST Transparency Portal https://seffaflik.epias.com.tr/transparency/

: From the description I am not sure that I understnad what simulation is being proposed. What will the simulation actully look like, what is it going simulate exactly? If you want to take into consideration the effcts like the Effects of Natural Gas Shortages, how will you quantify the strentg of such effect? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 21:47, 17 December 2022 (CET)

== Profit in store vs e-shop ==

''' Method:''' System Dynamics

'''Software:''' Vensim

'''Simulation'''

An unnamed company that sells carpets has its own store in Prague. During COVID-19 the company reopened an e-shop, so it currently has two mutually supporting sales channels. Both types of stores have their advantages and disadvantages. At the same time, there are various factors that affect the profit. Examples of these factors are the following: customer satisfaction and needs (carpet quality, order processing speed, price, etc.), expenses (advertising, rent, employees, etc.), the possibility of expansion, etc. To ensure customer satisfaction the company should make some expenses.

'''Model parameters'''

*Expenses
**fixed
**variable
*Revenues
**customer satisfaction -> influence amount of expenses
***Product quality,
***Speed of orders/purchases processing,
***Opening hours, working on weekends and holidays,
***The possibility of picking up the order in the store/speed of delivery
***Increasing customer satisfaction using sales and giving gifts for the order
***Store availability
***Parking
***Complaints fees
***Services: floor coverings including consultations and estimates, whipstitch of carpet
**price
**a number of sales, etc.

''' The goal of the simulation '''

The goal of this simulation is to find out what parameters can increase profit the most (individually for each type of store), to find a balance between expenses to satisfy the customers in order to achieve the profit, and in the end to compare these parameters.

'''Data'''

Real data provided by the owners of the store

[[User:Ploo00|Ploo00]] ([[User talk:Ploo00|talk]]) 01:41, 16 December 2022 (CET)
:Please elaborate in more detail as we have discussed in class [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 07:17, 17 December 2022 (CET)
::I changed the assignment a little bit. Can you please look at it? [[User:Ploo00|Ploo00]] ([[User talk:Ploo00|talk]]) 19:50, 17 December 2022 (CET)
::: If you have the data to derive the parameters from, than '''Approved'''. Describe in the report how you have derived the effects of and on the customer satisfaction. [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 21:52, 17 December 2022 (CET)

==Comparison of strategies for finding a lost person in the forest==

''' Author:''' Tomáš Kadaně (kadt02)

'''Type:''' Multi-agent

'''Software:''' NetLogo

'''Description:'''

The simulation will focus on comparing the times needed to find a lost person in a forest (area with trees).
The metric to compare the strategies will be the number of ticks needed to find the wanted person. Both the person being searched for and the searcher will be in a random location at the beginning of the simulation.
Within the simulation, I will take several measurements for each strategy and number of searchers (1 to 5), so that the number is statistically significant and use, for example, the means to compare which strategy is the most appropriate.

The model will be able to simulate several search strategies

*one step forward and then turn of random degree (-45 to 45 degrees), so random walk
*walk straight until it hits the edge of the forest or tree, then turn and continue walking straight
*first walk to the nearest corner of the forest and then a some kind of serpentine search
*possibly other strategies

'''Goals:'''

Finding the most appropriate strategy for finding a person in the forest depending on the number of people searching.

'''Agents:'''

*Searchers (e.g. police officers)
*Lost person

'''Parameters:'''

*Number of searchers
*Type of strategy
*Ticks needed to find person

'''Possible extensions:'''

*Searchers with certain pace of walking
*Finding the person won’t mean be at same location but seeing it for some distance (again certain ability of the searcher to see for certain distance)
*Cooperation of finders (formations, place distribution)
*Lost person will be moving when being looked for

[[User:Kadt02|Kadt02]] ([[User talk:Kadt02|talk]]) 16:01, 17 December 2022 (CET)

==Saving for an apartment==

Author: miln02

'''Problem definition'''

Jon has finally graduated to be an engineer and has found his first job. As he is living with his parents and doesn’t own his apartment, he made the decision to start saving so he can buy an apartment in the next 15 years. He already has some money that he has saved so far just sitting in his bank account, so he will use that as an initial investment, and after that he will invest a fixed amount every year.
He now must make a very important decision. Where should he invest his money? After doing some research, he focused on choosing between four different options:

1. Deposit money in the bank.

2. Purchase government bonds.

3. Invest in one of the world indices.

4. Invest all the money in one stock.

'''Goal'''

Create simulation that can be used as a support when making investment decision.

'''Method'''

For helping Jon to make a decision, I will use Monte Carlo simulation and Excel as an environment. The historical yield and volatility data will be used to calculate the average behaviour of all 4 options, and we will simulate possible results after 15 years. Since it can’t be expected that the market will be stable for all 15 years, economic crises will be generated.

'''Model parameters'''

* Investments:

-Initial one-time investment

-Fixed annual investment

* Market data:

-Deposits (Rate)

-Government bonds (Yield, volatility)

-Index (Yield, volatility)

-Stock (Yield, volatility)

* Economic crises probability

'''Sources'''

* https://finance.yahoo.com/

* http://www.worldgovernmentbonds.com/

* Bank website for deposit rates

[[User:Miln02|Miln02]] ([[User talk:Miln02|talk]]) 16:17, 17 December 2022 (CET)
:: '''Approved''' [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 22:14, 17 December 2022 (CET)

<nowiki>~~~~</nowiki>

==Test Proposal==
Author: Julian Bleyer

''' Simulation '''

''' Goal'''

''' Practical relevance '''

''' Method '''

''' Sources '''

==Car Park Solution for a New Cinema==
Author: kane02

'''Problem definition'''

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

'''Goal'''

1. Create simulation that optimizes the potential waiting time, price, and number of the parking space for stake holders.
2. Offer solution on how to increase profits.

'''Method'''

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

'''Model parameters'''

1. Park Timer
a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing
a. Set up rates per hours
b. Conditions on specific days
3. Reservation and Allocation
a. Reservation timer will adjust the potential waiting timer
b. When space is reserved new set of behaviour and conditions apply but price is fixed
''' Sources '''

https://ccl.northwestern.edu/netlogo/models/

https://jmvidal.cse.sc.edu/netlogomas/

[[User:Kane02|Kane02]] ([[User talk:Kane|talk]]) 14:10, 18 December 2022 (CET)

<nowiki>~~~~</nowiki>

Assignments WS 2022/2023

2022-12-18T13:02:33Z

Kane02:

Assignments WS 2022/2023

2022-12-18T13:00:21Z

Kane02:

{{Ambox
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Please, put here your assignments. Do not forget to sign them. You can use <nowiki>~~~~</nowiki> (four tildas) for an automatic signature. Use Show preview in order to check the result before your final sumbition.
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{{Ambox
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Please, strive to formulate your assignment carefully. We expect an adequate effort to formulate the assignment as it is your semestral paper. Do not forget that your main goal is a research paper. It means your simulation model must generate the results that are specific, measurable and verifiable. Think twice how you will develop your model, which entities you will use, draw a model diagram, consider what you will measure. No sooner than when you have a good idea about the model, submit your assignment. And of course, read [[How to deal with the simulation assignment|How to deal with the simulation assignment]].
</div>
}}

{{Ambox
| text = <div>
Topics on gambling, cards, etc. are not welcome.
</div>
}}

{{Ambox
| type = content
| text = <div>
In order to avoid possible confusion, please, check if you have added '''approved''' in bold somewhere in our comment under your submission. If there is no '''approved''', it means the assignment was not approved yet.
</div>
}}

== Effect of leniency programs on cartel rates by [[User:Baumareb|Baumareb]] ([[User talk:Baumareb|talk]]) 11:18, 7 December 2022 (CET) ==

''' Simulation '''

The leniency program of the European Commission offers the companies involved in a cartel either complete or partial immunity from fines if they self-report and hand over evidence. It was introduced in 1996, following the surge in amnesty applications in the wake of the 1993 revision of the Corporate Leniency Program of the US Department of Justice’s Antitrust Division. Reports from various implemented leniency programs showed that such programs led to numerous applications. However, despite the clear increase in leniency applications, the question poses itself as to whether the programs were also successful in a sense that the actual cartel rate in those countries declined.
The simulation will be based on a study of Harrington and Chang from 2015, in which they concluded the following:

• The actual cartel rate decreases in case that the leniency program does not affect the non-leniency enforcement

• But: if the non-leniency enforcement is affected because resources are shifted to the prosecution of leniency application cases, there might be two possibilities, the cartel rate might increase.

This simulation focuses on the latter case. Assuming endogenized non-leniency enforcement, the introduction of a leniency program might have a differential impact on different industries. If a leniency program is introduced, the cartels that are about to collapse will seek to self-report. This in turn shifts resources from exposing active cartels to prosecuting cartels that are already collapsing. This creates more work for the authorities, who, instead of focusing on active cartels may now focus on dying cartels. This crowding-out effect coming about with the introduction of a leniency program shall be simulated in this project.

''' Goal '''

The simulation will have the following objectives:

* Illustrate the change in cartel rates and the change in the average life expectancy of a cartel triggered by the introduction of a leniency program in case of endogenized non-leniency enforcement for industries with unstable cartels (e.g. industries with a high number of competitors, or demand with more price elasticity) and for industries with stable cartels (e.g. industries with less competitors and demand with less price elasticity).
* Illustrate how many resources may be shifted from non-leniency enforcement to prosecuting leniency application cases without it having an undesired effect on the actual cartel rate.

''' Practical relevance '''

The simulation may be used by law enforcement officials to evaluate whether a leniency program leads to the desired effect (i.e. the decrease in the cartel rate) or not. Also, it can help for deciding whether the non-leniency enforcement needs to be strengthened to prevent the crowding-out effect.

''' Method '''

The described scenario is a multi-agent simulation in which the agents are pursuing a utility-based approach. Thus, the simulation will be done with NetLogo.
The following features will be included into the simulation:

- For both industries with stable and industries with unstable cartels:

* Number of active cartels (dying after reaching avg. life expectancy)
* Number of competitors
* Average life expectancy of a cartel
* “Birth” of new cartels

- For leniency/non-leniency enforcement:
* Resources and their assignment to either leniency or non-leniency enforcement
* Capacity of taking down an active cartel
* Capacity of taking down a cartel based on leniency applications

The simulation will be based on the 2015 research from Harrington and Chang as well as on publicly accessible data from the European Commission regarding antitrust cases from 1964 until today.

''' Sources '''
* Harrington Jr, J. E., & Chang, M. H. (2015). When can we expect a corporate leniency program to result in fewer cartels?. The Journal of Law and Economics, 58(2), 417-449.
* Ordóñez‐De‐Haro, J. M., Borrell, J. R., & Jiménez, J. L. (2018). The European commission's fight against cartels (1962–2014): A retrospective and forensic analysis. JCMS: Journal of Common Market Studies, 56(5), 1087-1107.

[[User:Baumareb|Baumareb]] ([[User talk:Baumareb|talk]]) 11:18, 7 December 2022 (CET) Rebecca Baumann (baur00)

: This isn't an easy topic. Be careful about available data. '''Approved''' [[User:Tomáš|Tomáš]] ([[User talk:Tomáš|talk]]) 01:46, 15 December 2022 (CET)

== The prediction of divorce rate in Czech Republic for the following 50 years ==

''' The goal of the simulation '''

Divorce in the Czech republic must always contain at least one hearing in front of the court. Legally, there are many more parties involved, such as a notary, who must verify the signatures on all the important documents and many times, divorce lawyers are also necessary. To be able to satisfy the needs of the public, all the involved parties must have an idea about how many married couples are likely to get divorced in the years to come. This simulation will help prepare the courts, notaries and lawyers by making a prediction on the amount of divorces in the next 50 years. This will also help law students choose the field of law that they will specialize in by answering the question whether divorce lawyers will be necessary in the future or not.

''' Method '''

Vensim will be used for this simulation. The used data will come from the Czech Statistical Office and possibly other sources (Refer to [1] and [2]), such as published studies on the most common reasons for divorce. When possible, the data about each reason of divorce will be also found and the simulation model will contain this data.

== Edit: additional details ==

''' What all parameters will the simulation work with and how?'''

1. Number of marriages – the more marriages, the more divorces

a/ Number of people in the age 25 to 34 (i.e., the most common age to get married) – the more there is of these people, the more marriages there will be

b/ Number of divorced people in the age 40 to 49 (i.e., the most common age to get re-married after a divorce) – the more there is of these people, the more marriages there will be, however not as much as the number above

2. Micro causes of divorces = Top 10 causes of divorce as researched by the Czech Statistical Office, published yearly – the more common are these causes (alcoholism, infidelity etc), the more divorces there will be

a/ Ill-considered marriage

b/ Alcoholism

c/ Infidelity

d/ Lack of interest in the family (incl. abandon. of living together)

e/ Ill-treatment, criminal conviction

f/ Different characters, views and interests

g/ Health reasons

h/ Sexual discord

i/ Other causes

j/ Cause not given

3. Number of people in the age 40 to 49 – the more there is of these people, the more divorces there will be (it is the most common age to get divorced)

4. Macro causes of divorces

a/ Economic independence of women = the more economically independent women are, the more likely they are to divorce in case of an unhappy marriage – this will be evaluated through a comparison of data of average income of men vs. women

b/ Being religious – divorce is far less common for religious people.

''' What data source will be used for deriving the equations?'''

Based on my current research of data sources, the Czech Statistical Office has the all the data necessary for this paper.

[1] Scott, S. B., Rhoades, G. K., Stanley, S. M., Allen, E. S., & Markman, H. J. (2013). Reasons for Divorce and Recollections of Premarital Intervention: Implications for Improving Relationship Education. Couple & family psychology, 2(2), 131–145. https://doi.org/10.1037/a0032025

[2] Hawkins, Alan & Willoughby, Brian & Doherty, William. (2012). Reasons for Divorce and Openness to Marital Reconciliation. Journal of Divorce & Remarriage. 53. 453-463. 10.1080/10502556.2012.682898.

: Sounds interesting, but I miss more detail about the simulation. What all parameters will the simulation work with and how? What data source will be used for deriving the equations? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 11:03, 15 December 2022 (CET)
:: ''' Approved'''. Just make sure that the equtions, reasons for divorce and their impact on divorce rate are properly quantified.[[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 07:23, 17 December 2022 (CET)

==Crop Yield Forecasting==

''' Simulation '''

Crop growth and development simulations and yield forecasting will be performed using variables such as crop type, planting date, soil type, soil texture, and climate data (temperature, rainfall, etc.).

'''Problem definition'''

Arable land is increasingly limited, while the world's population has steadily been increasing over the years. In order to meet rapidly rising demand, production must be increased while natural resources must be protected. New agricultural research is needed to provide information on how to achieve sustainable agriculture in the face of global climate variability. Predicting crop yield under different conditions, such as different irrigation regimes, planting dates, and crop management practices, has become critical for farmers and other stakeholders who use these predictions to make more informed decisions about how to allocate resources, such as labor, equipment, and inputs, to maximize yield and productivity.

'''Method'''

Crop yield simulation tools include AquaCrop, DSSAT, and CropSyst. These tools use mathematical models to simulate crop growth and development based on input data like weather, soil type, and management practices. These tools use this data to estimate the crop's potential yield, as well as other important factors like water use and crop evapotranspiration. For this assignment I will be using AquaCrop which is a crop water productivity model developed by the United Nations Food and Agriculture Organization (FAO). It is used to simulate crop growth and yield under various environmental and management conditions. AquaCrop simulates crop growth and development, and estimates yield based on soil conditions, climate, irrigation, and management practices. The application gives access to various FAO databases with all the necessary data needed to perform a comprehensive simulation of the crop yield.

'''Citations'''

* Y. Lu, C. Wei, M. F. McCabe, and J. Sheffield, “Multi-variable assimilation into a modified AquaCrop model for improved maize simulation without management or crop phenology information,” Agricultural Water Management, vol. 266, p. 107576, May 2022, doi: 10.1016/j.agwat.2022.107576.
* P. N. Kephe, K. K. Ayisi, and B. M. Petja, “Challenges and opportunities in crop simulation modelling under seasonal and projected climate change scenarios for crop production in South Africa,” Agriculture & Food Security, vol. 10, no. 1, p. 10, Apr. 2021, doi: 10.1186/s40066-020-00283-5.
* N. T. Olivera, O. B. Manrique, Y. G. Masjuan, and A. M. G. Alega, “Evaluation of AquaCrop model in crop dry bean growth simulation,” Revista Ciencias Técnicas Agropecuarias, vol. 25, no. 3, pp. 23–30, Accessed: Dec. 10, 2022. [Online]. Available: https://www.redalyc.org/journal/932/93246970003/html/
* N. Pirmoradian, Z. Saadati, M. Rezaei, and M. R. Khaledian, “Simulating water productivity of paddy rice under irrigation regimes using AquaCrop model in humid and semiarid regions of Iran,” Appl Water Sci, vol. 10, no. 7, p. 161, Jun. 2020, doi: 10.1007/s13201-020-01249-5.

[[User:Pierreatekwana|Pierreatekwana]] ([[User talk:Pierreatekwana|talk]]) 15:06, 15 December 2022 (CET)

: Topic souds interesting, but the proposed simulation tool has to be one of the ones we have used in our class ( as specified in How to deal with the simulation assignment:
One of your key course requirements is a submission of simulation. You choose your topic yourself, the same as a method and a tool that you will use. It could be any of the development environments we have used (Excel, Simprocess, Netlogo, or Vensim).) [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 07:05, 17 December 2022 (CET)

== Electricity Spot Market Simulation by [[User:Ceta|Ceta]] ([[User talk:Ceta|talk]]) 01:13, 16 December 2022 (CET) ==

== IDEA 1 ==

'''Problem definition'''

Anthony is as a portfolio manager in the power company Goodpower. Goodpower has a portfolio of power plants. Goodpower is a market participant in a liberated market structure. The power generation can be sold either in spot market with volatile prices, or it can be sold with a yearly fixed price on over the counter (OTC). Goodpower assigned Anthony responsible for optimization of power generation revenue. Now Anthony needs to decide on how much generation to risk in the volatile spot market and how much to risk with the fixed price. After contacting the power brokers in OTC market, he was offered the following deals:

1. A baseload deal with a fixed price.

2. An off-peak hours deal with a fixed price.

3. A peak hours deal with a fixed price.

'''Goal'''

Simulation that can be used as a decision support tool when managing a power portfolio.

'''Method'''

Monte Carlo simulation in Excel environment will be created. The historical spot prices will be used to determine fixed deal prices. The historical generation values will be used to determine generation scenarios (wet season - high.generation, average generation, dry season – low generation). The volatility of spot market prices will be based on again historical spot prices. The simulation of 1 year = 8760 hours will be generated. Since, the stability spot market prices in winter are dependent on natural gas shortages, these shortage scenarios will be added to the simulation.

'''Model parameters'''

• Generation scenarios:

- Wet season – high generation (MWh)

- Average season - average generation (MWh)

- Dry season – low generation (MWh)

• Market data:

- Volatile spot market prices (USD/MWh)

- Fixed deal prices will be based on past year spot market prices (While OTC market prices can’t be publicly viewed)

''' Data '''

- EXIST Transparency Portal https://seffaflik.epias.com.tr/transparency/

: From the description I am not sure that I understnad what simulation is being proposed. What will the simulation actully look like, what is it going simulate exactly? If you want to take into consideration the effcts like the Effects of Natural Gas Shortages, how will you quantify the strentg of such effect? [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 21:47, 17 December 2022 (CET)

== Profit in store vs e-shop ==

''' Method:''' System Dynamics

'''Software:''' Vensim

'''Simulation'''

An unnamed company that sells carpets has its own store in Prague. During COVID-19 the company reopened an e-shop, so it currently has two mutually supporting sales channels. Both types of stores have their advantages and disadvantages. At the same time, there are various factors that affect the profit. Examples of these factors are the following: customer satisfaction and needs (carpet quality, order processing speed, price, etc.), expenses (advertising, rent, employees, etc.), the possibility of expansion, etc. To ensure customer satisfaction the company should make some expenses.

'''Model parameters'''

*Expenses
**fixed
**variable
*Revenues
**customer satisfaction -> influence amount of expenses
***Product quality,
***Speed of orders/purchases processing,
***Opening hours, working on weekends and holidays,
***The possibility of picking up the order in the store/speed of delivery
***Increasing customer satisfaction using sales and giving gifts for the order
***Store availability
***Parking
***Complaints fees
***Services: floor coverings including consultations and estimates, whipstitch of carpet
**price
**a number of sales, etc.

''' The goal of the simulation '''

The goal of this simulation is to find out what parameters can increase profit the most (individually for each type of store), to find a balance between expenses to satisfy the customers in order to achieve the profit, and in the end to compare these parameters.

'''Data'''

Real data provided by the owners of the store

[[User:Ploo00|Ploo00]] ([[User talk:Ploo00|talk]]) 01:41, 16 December 2022 (CET)
:Please elaborate in more detail as we have discussed in class [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 07:17, 17 December 2022 (CET)
::I changed the assignment a little bit. Can you please look at it? [[User:Ploo00|Ploo00]] ([[User talk:Ploo00|talk]]) 19:50, 17 December 2022 (CET)
::: If you have the data to derive the parameters from, than '''Approved'''. Describe in the report how you have derived the effects of and on the customer satisfaction. [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 21:52, 17 December 2022 (CET)

==Comparison of strategies for finding a lost person in the forest==

''' Author:''' Tomáš Kadaně (kadt02)

'''Type:''' Multi-agent

'''Software:''' NetLogo

'''Description:'''

The simulation will focus on comparing the times needed to find a lost person in a forest (area with trees).
The metric to compare the strategies will be the number of ticks needed to find the wanted person. Both the person being searched for and the searcher will be in a random location at the beginning of the simulation.
Within the simulation, I will take several measurements for each strategy and number of searchers (1 to 5), so that the number is statistically significant and use, for example, the means to compare which strategy is the most appropriate.

The model will be able to simulate several search strategies

*one step forward and then turn of random degree (-45 to 45 degrees), so random walk
*walk straight until it hits the edge of the forest or tree, then turn and continue walking straight
*first walk to the nearest corner of the forest and then a some kind of serpentine search
*possibly other strategies

'''Goals:'''

Finding the most appropriate strategy for finding a person in the forest depending on the number of people searching.

'''Agents:'''

*Searchers (e.g. police officers)
*Lost person

'''Parameters:'''

*Number of searchers
*Type of strategy
*Ticks needed to find person

'''Possible extensions:'''

*Searchers with certain pace of walking
*Finding the person won’t mean be at same location but seeing it for some distance (again certain ability of the searcher to see for certain distance)
*Cooperation of finders (formations, place distribution)
*Lost person will be moving when being looked for

[[User:Kadt02|Kadt02]] ([[User talk:Kadt02|talk]]) 16:01, 17 December 2022 (CET)

==Saving for an apartment==

Author: miln02

'''Problem definition'''

Jon has finally graduated to be an engineer and has found his first job. As he is living with his parents and doesn’t own his apartment, he made the decision to start saving so he can buy an apartment in the next 15 years. He already has some money that he has saved so far just sitting in his bank account, so he will use that as an initial investment, and after that he will invest a fixed amount every year.
He now must make a very important decision. Where should he invest his money? After doing some research, he focused on choosing between four different options:

1. Deposit money in the bank.

2. Purchase government bonds.

3. Invest in one of the world indices.

4. Invest all the money in one stock.

'''Goal'''

Create simulation that can be used as a support when making investment decision.

'''Method'''

For helping Jon to make a decision, I will use Monte Carlo simulation and Excel as an environment. The historical yield and volatility data will be used to calculate the average behaviour of all 4 options, and we will simulate possible results after 15 years. Since it can’t be expected that the market will be stable for all 15 years, economic crises will be generated.

'''Model parameters'''

* Investments:

-Initial one-time investment

-Fixed annual investment

* Market data:

-Deposits (Rate)

-Government bonds (Yield, volatility)

-Index (Yield, volatility)

-Stock (Yield, volatility)

* Economic crises probability

'''Sources'''

* https://finance.yahoo.com/

* http://www.worldgovernmentbonds.com/

* Bank website for deposit rates

[[User:Miln02|Miln02]] ([[User talk:Miln02|talk]]) 16:17, 17 December 2022 (CET)
:: '''Approved''' [[User:Oleg.Svatos|Oleg.Svatos]] ([[User talk:Oleg.Svatos|talk]]) 22:14, 17 December 2022 (CET)

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==Test Proposal==
Author: Julian Bleyer

''' Simulation '''

''' Goal'''

''' Practical relevance '''

''' Method '''

''' Sources '''

==Car Park Solution for a New Cinema==
Author: kane02

'''Problem definition'''

A brand-new cinema is opening at Vypich in 6 months at one of the busiest streets in the region. The ambitious owners decided to use their extra budget to operate a small parking space right in front of the cinemas entrance for providing a space to park for customers and generate further profits. Planned parking space will have fixed expense for each month but the land itself can be extended. Owners are now in need of expertise on how to approach this issue. Their requirements consist of.

1. Counter on when a car enters and departs.
2. Create a receipt depending on hours.
3. Take reservations and allocate the space.

'''Goal'''

1. Create simulation that optimizes the potential waiting time, price, and number of the parking space for stake holders.
2. Offer solution on how to increase profits.

'''Method'''

For getting the job done I shall be using NetLogo to create the simulation based on client-side metrics and goals.

'''Model parameters'''

Model parameters
1. Park Timer
a. Counter for calculating total minutes
b. Boolean checker for availability
2. Billing
a. Set up rates per hours
b. Conditions on specific days
3. Reservation and Allocation
a. Reservation timer will adjust the potential waiting timer
b. When space is reserved new set of behaviour and conditions apply but price is fixed
''' Sources '''

https://ccl.northwestern.edu/netlogo/models/

https://jmvidal.cse.sc.edu/netlogomas/

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