Rubinstein Bargaining - Revision history

Kane02: Blanked the page

2023-02-01T19:02:50Z

Blanked the page

Show changes

Kane02 at 11:24, 14 January 2023

2023-01-14T11:24:51Z

Kane02 at 11:23, 14 January 2023

2023-01-14T11:23:11Z

Kane02 at 11:16, 14 January 2023

2023-01-14T11:16:27Z

Kane02 at 11:14, 14 January 2023

2023-01-14T11:14:32Z

Kane02 at 10:45, 14 January 2023

2023-01-14T10:45:28Z

Kane02 at 10:33, 14 January 2023

2023-01-14T10:33:39Z

Kane02 at 10:33, 14 January 2023

2023-01-14T10:33:14Z

Kane02 at 10:31, 14 January 2023

2023-01-14T10:31:06Z

Kane02 at 21:51, 13 January 2023

2023-01-13T21:51:58Z

@@ Line 154: / Line 154: @@
 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=
 <references/>

@@ Line 150: / Line 150: @@
 =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.
+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="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>.
+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/>

@@ Line 10: / Line 10: @@
 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
+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>.
@@ Line 16: / Line 16: @@
 * 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>.
+* 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="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>.
+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):
@@ Line 68: / Line 68: @@
 The solution of the Rubinstein bargaining model is determined by the following formulas:
-. 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:
+. 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:
@@ Line 152: / Line 152: @@
 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>.
+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>.

@@ Line 10: / Line 10: @@
 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.
+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
 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.
+* 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.
+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):
@@ Line 38: / Line 39: @@
 =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.
+[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=
@@ Line 60: / Line 61: @@
 =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.
+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.
@@ Line 67: / Line 68: @@
 The solution of the Rubinstein bargaining model is determined by the following formulas:
-. 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:
+. 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:
@@ Line 151: / Line 152: @@
 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.
+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>.

← Older revision		Revision as of 10:45, 14 January 2023
Line 57:		Line 57:

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

@@ Line 45: / Line 45: @@
 . 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.
 . Allows for calculating the Nash Bargaining Solution, a unique and efficient solution for both parties involved in the negotiation.
 . Helps to identify the optimal outcome for both parties involved in the negotiation, which can lead to mutually beneficial agreements.
 . Applicable to various negotiation scenarios, making it a versatile tool for understanding negotiations.
 . Can be used to identify potential sources of conflict and design negotiation strategies to mitigate or avoid them.
 . It is used to understand the role of different factors, such as the outside options and reservation values, in the negotiation process.
 . Researchers have extensively studied and validated it, providing a solid theoretical foundation for its use in real-world negotiations.

@@ Line 36: / Line 36: @@
 '''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.
-=Understanding the Procedure of Barganing=
+=Nash Equilibrium Condition=
-Before discovering further deep concepts, a quick and simple example about Rubinstein Barganing:
+[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.
-'''Setup for the Game Example: '''
+=Benefits of Rubinstein Bargaining=
-we have an infinite horizon game between two players call him Dave and Sally and in all odd periods, Dave will make an offer to Sally, which Sally accepts or rejects, and in all even periods. Sally makes an offer to Dave which Dave accepts or rejects, the game continues until one player accepts when that player accepts that's the division and the game ends and as long as the players keep rejecting then we keep moving to the next period, where the other players will make the offer and we'll keep doing that until one of them finally accepts, and if no one ever accepts, then the payoffs are just zero for both players
+The Rubinstein bargaining model has several benefits and positives:
-* Odd Periods, Dave makes an offer
+=General Solution=
-Rubinstein bargaining alternatively picks up on is the idea that when we're in this situation at a bargaining discussion and it's never exactly clear who has that last offer,  opposed to a game with an arbitrary fixed cutoff to the negotiations. This feature is called '''Stationary Strategies'''
+The solution of the Rubinstein bargaining model is determined by the following formulas:
-Stationary Strategy is a strategy that doesn't change from period to period when those periods are identical so all odd periods here are identical and all odd periods Dave is making an offer to Sally which Sally accepts or rejects and all the even periods are identical as well and there we have Sally making an offer to Dave which Dave accepts or rejects.
+. 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:
-* Solution: Rubinstein bargaining can conceivably go on forever, meaning there is no fixed ending period that can start at and work the way back. start off by taking Sally's continuation value for some odd period as a value known as VB. so what is this continuation value well it's the non discounted amount she will receive if no agreement is made in the current period
+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.