Simulace.info - User contributions [en]

Multistage Games

2014-02-02T20:35:38Z

Xklit17:

__TOC__
==Introduction==
[[Normal form|Normal-form games]] models a game where players choose their moves simultaneously without observing other players moves. [[Extensive form|Extensive-form games]] adds a possibility playing sequentially - allowing players to learn about the choices of previous players, so the player can condition his moves based on previous players decisions. [[Extensive form|Extensive-form games]] have their payoff expressed after the end of the game (one "grand game"). In reality, dynamic play over time may be more complex than one game that unfolds over time. Instead, players can play one game that is followed by another, or maybe even several other games.

* Should we consider each game independently, or should we expect players to consider the sequence of different games as one "grand game"?
* How to evaluate total payoffs from a sequence of payoffs in each of the sequentially played stage-games? What is the value of payoff in period ''N'' and in period ''N+20''? If it was just a one-stage-game we could "solve" the game using Weak Perfect Bayesian Equilibrium...
* Will the players moves vary if the stage-game were not played sequentially but as independent games?
* Will a player vary from the stage-game [[Nash equilibrium]] to a different action, which will result him a higher payoff in the following stage-games?

==Definitions==
===Multi-stage game===
A definition of multi-stage game by S. Tadelis is following: A multi-stage game is '''a finite sequence of stage-games''', each one being a game of '''complete but imperfect information''' (a '''simultaneous move game'''). These games are '''played sequentially by the same players''', and the total payoffs from the sequence of games will be evaluated using the sequence of outcomes in the games that were played. We adopt the convention that each game is played in a distinct period, so that game 1 is played in period 1, game 2 in period 2, and so on. We will also assume that after each stage is completed, all the players observe the outcome of that stage, and that this information structure is common knowledge. <ref name="Tadelis2013">Tadelis, Steve. ''Game Theory: An Introduction.'' Princeton: Princeton UP, 2013. Print.</ref>

Multi-stage game consists of multiple games. In each game, players have a set of action they choose from, and the profiles of actions lead to payoffs for that specific game, which is then followed by another game and another, until sequence of games is over. Once we realize that one game follows another, this implies that players can observe the outcomes of each game before another game is played. This observation is important because it allows players to condition their future actions on past outcomes. This is the idea at the center of multi-stage games: the ability to condition behavior may lead to a rich set of outcomes. In what follows, we will analyze the idea of conditional strategies, and the equilibrium that can be supported using such strategies.<ref name="Tadelis2013" />

Other sources use term Multi-stage game with a wider meaning including also games with Perfect Information <ref>Rosu, Ioanid. "Multi-Stage Game Theory in Continous Time." Ioanid Rosu - Research. HEC Paris, 1 Jan. 2006. Web. 2 Feb. 2014.</ref> which is in contrary to the <ref name="Tadelis2013" />. Following material uses definition of S. Tadelis, which is mentioned above.

===Information Set===
[[File:Information-set.png|200px|thumb|right|Information set (dashed blue line)]]
Information Set is collection of decision nodes such that:
* When the play reaches a node in the information set, the player with the move does not know which node in the information set has been reached.
* The player has the same set of choices at each node in the information set.

Information Set can be used in [[Extensive form|extensive-form games]] to view a subgame with simultaneous moves of the players. If the player doesn't have the same set of choices at each node it is not an Information set. The point is that for the player its unknown and undecidable know at what node we are. Why is Information Set used? Because it allows us to view a complicated multi-stage game in a familiar tree view, which is also used in Dynamic Games.

==Conditional strategies==
If a multistage game consists of N games and we break up the games into N individual games and take it as an individual game. And if the players won't try to link them in any way, then the strategies would be pretty simple - each game is treated independently and each player chooses its best strategy to get the highest payoff in the respective stage game.

But in case of a multi-stage game players may want to link the individual games and create a strategy that will yield the best payoff. A simple example of linking different games can be following - If you play a game of chess with me now, I'll go with you to a cinema. If not, I won't go with you. Which generally means using strategies in form of "if A happens in games 1,2... n-1 then I will choose this action in game N". A simple way to explain conditional strategies is to take one of the below examples and write all extensive forms of strategies - "I will play F in the first game and I will play L in the second game only if player 2 played M in the first game. If player 2 played F in the first game then I will play G in the second."

To decide which Strategy would be the best to play for both of the players - similar to finding equilibrium like [[Nash equilibrium]], we would have to introduce Sequential Equilibrium. <ref>David M. Kreps and Robert Wilson. ''Sequential Equilibria'', Econometrica 50:863-894, 1982.</ref> Sequential Equilibrium does specify a strategy for each player and a belief for each of the players. A belief gives, for each information set of the game belonging to the player, a probability distribution on nodes in the information set (see [[Bayesian Equilibrium]]).

==Payoffs==
How to evaluate total payoffs from all of the N stage-games? Is it a simple sum of all of the payoffs from all the stage-games? There is a well defined notion from economic analysis (and standard cost-benefit analysis) of present value which should be used to calculate the total payoff. <ref name="Tadelis2013" />

It is easy to justify the assumption that payoffs obtained in earlier stage-game are worth more than payoffs obtained in later stage-games. Take in consideration financial markets - if a game played today yield a payment of 20 and another is played in a year and it will also yield 20, then today's value of the second payment will be worth less than 20. Say there is a 10% interest rate at which we can borrow money then we can borrow 20 today and repay 22 in a year, which is the future payoff from the game. So the 22 next year is worth exactly 20 today. Alternatively you can use analogy with discount, which you should be definitely familiar with. Another way to justify the assumption of discounting, or ''impatience'', is that today's game is played now and its not 100% certain that the next will be played. For example if two players are playing a game in period one, there may be some probability that tomorrow's game won't be played. Then the payoff of the first game is more reliable and has a higher momentary value independent from the occurrence of the second game, because you have to take in account the probability of not-playing the game, ergo not getting the money.

For more detailed information about calculating the Total Payoff using discounted sum of payoffs that the player expects to get in the sequence of all stage-games see the <ref name="Tadelis2013" />. But the idea is pretty simple - The payoffs in one period away are discounted once, two periods away are discounted twice and so on.

==Subgame Perfect Equilibria==
[[File:Two-stage-game.png|150px|thumb|right|Simple two-stage game]]
Since multi-stage games are dynamic in nature, and the past play is revealed over time, it is natural to turn to Subgame Perfect Equilibrium (SPE) as a solution concept. In particular, rational players should play sequentially rational strategies, which justifies the concept of SPE, and because total payoffs are defined above we are able to use it.

Example of a simple two-stage game of two players from <ref name="Tadelis2013" /> is shown on the side, number of possible pure strategies is 32x32 = 1024! If we cannot relay on playing sequentially rational strategies we should turn to the Sequential Equilibrium mentioned above.

==Example - Extensive game with simultaneous moves<ref name="Osborne" />==
[[File:Extensive game with simultaneousmoves.png|200px|thumb|right|Extensive game with simultaneous moves<ref name="Osborne">Osborne, Martin J. An Introduction to Game Theory. New York: Oxford UP, 2004. Print.</ref>]]
The subgame following player 1’s choice of A has two Nash equilibria, (C, C) and (D, D); the subgame following player 1’s choice of B also has two Nash equilibria, (E, E) and (F, F). If the equilibrium reached after player 1 chooses A is (C, C), then regardless of the equilibrium reached after she chooses (E, E), she chooses A at the beginning of the game. If the equilibrium reached after player 1 chooses A is (D, D) and the equilibrium reached after she chooses B is (F, F), she chooses A at the beginning of the game. If the equilibrium reached after player 1 chooses A is (D, D) and the
equilibrium reached after she chooses B is (E, E), she chooses B at the beginning of the game.

Thus the game has four subgame perfect equilibria: (ACE, CE), (ACF, CF), (ADF, DF), and (BDE, DE) (where the first component of player 1’s strategy is
her choice at the start of the game, the second component is her action after she chooses A, and the third component is her action after she chooses B, and the first component of player 2’s strategy is her action after player 1 chooses A at the start of the game and the second component is her action after player 1 chooses B at the start of the game).

In the first two equilibria the outcome is that player 1 chooses A and then both players choose C, in the third equilibrium the outcome is that player 1 chooses A and then both players choose D, and in the last equilibrium the outcome is that player 1 chooses B and then both players choose E.

==Questions==
# What is the difference between Multi-stage game and Repeated game?
# Is the total payoff of a multi-stage game a sum of all payoffs of all stage games?
# What is Information Set?
# How is Information Set relevant to Information completeness in extensive-form game.
# Is there an easy way "to solve" Multi-stage game?
# Name the characteristics of a Multi-stage game by S. Tadelis.

==References==
<references />

Multistage Games

2014-02-02T20:32:37Z

Xklit17:

__TOC__
==Introduction==
[[Normal form|Normal-form games]] models a game where players choose their moves simultaneously without observing other players moves. [[Extensive form|Extensive-form games]] adds a possibility playing sequentially - allowing players to learn about the choices of previous players, so the player can condition his moves based on previous players decisions. [[Extensive form|Extensive-form games]] have their payoff expressed after the end of the game (one "grand game"). In reality, dynamic play over time may be more complex than one game that unfolds over time. Instead, players can play one game that is followed by another, or maybe even several other games.

* Should we consider each game independently, or should we expect players to consider the sequence of different games as one "grand game"?
* How to evaluate total payoffs from a sequence of payoffs in each of the sequentially played stage-games? What is the value of payoff in period ''N'' and in period ''N+20''? If it was just a one-stage-game we could "solve" the game using Weak Perfect Bayesian Equilibrium...
* Will the players moves vary if the stage-game were not played sequentially but as independent games?
* Will a player vary from the stage-game [[Nash equilibrium]] to a different action, which will result him a higher payoff in the following stage-games?

==Definitions==
===Multi-stage game===
A definition of multi-stage game by S. Tadelis is following: A multi-stage game is '''a finite sequence of stage-games''', each one being a game of '''complete but imperfect information''' (a '''simultaneous move game'''). These games are '''played sequentially by the same players''', and the total payoffs from the sequence of games will be evaluated using the sequence of outcomes in the games that were played. We adopt the convention that each game is played in a distinct period, so that game 1 is played in period 1, game 2 in period 2, and so on. We will also assume that after each stage is completed, all the players observe the outcome of that stage, and that this information structure is common knowledge. <ref name="Tadelis2013">Tadelis, Steve. ''Game Theory: An Introduction.'' Princeton: Princeton UP, 2013. Print.</ref>

Multi-stage game consists of multiple games. In each game, players have a set of action they choose from, and the profiles of actions lead to payoffs for that specific game, which is then followed by another game and another, until sequence of games is over. Once we realize that one game follows another, this implies that players can observe the outcomes of each game before another game is played. This observation is important because it allows players to condition their future actions on past outcomes. This is the idea at the center of multi-stage games: the ability to condition behavior may lead to a rich set of outcomes. In what follows, we will analyze the idea of conditional strategies, and the equilibrium that can be supported using such strategies.<ref name="Tadelis2013" />

Other sources use term Multi-stage game with a wider meaning including also games with Perfect Information <ref>Rosu, Ioanid. "Multi-Stage Game Theory in Continous Time." Ioanid Rosu - Research. HEC Paris, 1 Jan. 2006. Web. 2 Feb. 2014.</ref> which is in contrary to the <ref name="Tadelis2013" />. Following material uses definition of S. Tadelis, which is mentioned above.

===Information Set===
[[File:Information-set.png|200px|thumb|right|Information set (dashed blue line)]]
Information Set is collection of decision nodes such that:
* When the play reaches a node in the information set, the player with the move does not know which node in the information set has been reached.
* The player has the same set of choices at each node in the information set.

Information Set can be used in [[Extensive form|extensive-form games]] to view a subgame with simultaneous moves of the players. If the player doesn't have the same set of choices at each node it is not an Information set. The point is that for the player its unknown and undecidable know at what node we are. Why is Information Set used? Because it allows us to view a complicated multi-stage game in a familiar tree view, which is also used in Dynamic Games.

==Conditional strategies==
If a multistage game consists of N games and we break up the games into N individual games and take it as an individual game. And if the players won't try to link them in any way, then the strategies would be pretty simple - each game is treated independently and each player chooses its best strategy to get the highest payoff in the respective stage game.

But in case of a multi-stage game players may want to link the individual games and create a strategy that will yield the best payoff. A simple example of linking different games can be following - If you play a game of chess with me now, I'll go with you to a cinema. If not, I won't go with you. Which generally means using strategies in form of "if A happens in games 1,2... n-1 then I will choose this action in game N". A simple way to explain conditional strategies is to take one of the below examples and write all extensive forms of strategies - "I will play F in the first game and I will play L in the second game only if player 2 played M in the first game. If player 2 played F in the first game then I will play G in the second."

To decide which Strategy would be the best to play for both of the players - similar to finding equilibrium like [[Nash equilibrium]], we would have to introduce Sequential Equilibrium. <ref>David M. Kreps and Robert Wilson. ''Sequential Equilibria'', Econometrica 50:863-894, 1982.</ref> Sequential Equilibrium does specify a strategy for each player and a belief for each of the players. A belief gives, for each information set of the game belonging to the player, a probability distribution on nodes in the information set (see [[Bayesian Equilibrium]]).

==Payoffs==
How to evaluate total payoffs from all of the N stage-games? Is it a simple sum of all of the payoffs from all the stage-games? There is a well defined notion from economic analysis (and standard cost-benefit analysis) of present value which should be used to calculate the total payoff. <ref name="Tadelis2013" />

It is easy to justify the assumption that payoffs obtained in earlier stage-game are worth more than payoffs obtained in later stage-games. Take in consideration financial markets - if a game played today yield a payment of 20 and another is played in a year and it will also yield 20, then today's value of the second payment will be worth less than 20. Say there is a 10% interest rate at which we can borrow money then we can borrow 20 today and repay 22 in a year, which is the future payoff from the game. So the 22 next year is worth exactly 20 today. Alternatively you can use analogy with discount, which you should be definitely familiar with. Another way to justify the assumption of discounting, or ''impatience'', is that today's game is played now and its not 100% certain that the next will be played. For example if two players are playing a game in period one, there may be some probability that tomorrow's game won't be played. Then the payoff of the first game is more reliable and has a higher momentary value independent from the occurrence of the second game, because you have to take in account the probability of not-playing the game, ergo not getting the money.

For more detailed information about calculating the Total Payoff using discounted sum of payoffs that the player expects to get in the sequence of all stage-games see the <ref name="Tadelis2013" />. But the idea is pretty simple - The payoffs in one period away are discounted once, two periods away are discounted twice and so on.

==Subgame Perfect Equilibria==
[[File:Two-stage-game.png|400px|thumb|right]]
Since multi-stage games are dynamic in nature, and the past play is revealed over time, it is natural to turn to Subgame Perfect Equilibrium (SPE) as a solution concept. In particular, rational players should play sequentially rational strategies, which justifies the concept of SPE, and because total payoffs are defined above we are able to use it. Example of a simple two-stage game of two players from <ref name="Tadelis2013" /> is shown on the side, number of possible pure strategies is 32x32 = 1024! If we cannot relay on playing sequentially rational strategies we should turn to the Sequential Equilibrium mentioned above.

==Example - Extensive game with simultaneous moves==
[[File:Extensive game with simultaneousmoves.png|400px|thumb|right]]
The subgame following player 1’s choice of A has two Nash equilibria, (C, C) and (D, D); the subgame following player 1’s choice of B also has two Nash equilibria, (E, E) and (F, F). If the equilibrium reached after player 1 chooses A is (C, C), then regardless of the equilibrium reached after she chooses (E, E), she chooses A at the beginning of the game. If the equilibrium reached after player 1 chooses A is (D, D) and the equilibrium reached after she chooses B is (F, F), she chooses A at the beginning of the game. If the equilibrium reached after player 1 chooses A is (D, D) and the
equilibrium reached after she chooses B is (E, E), she chooses B at the beginning of the game.

Thus the game has four subgame perfect equilibria: (ACE, CE), (ACF, CF), (ADF, DF), and (BDE, DE) (where the first component of player 1’s strategy is
her choice at the start of the game, the second component is her action after she chooses A, and the third component is her action after she chooses B, and the first component of player 2’s strategy is her action after player 1 chooses A at the start of the game and the second component is her action after player 1 chooses B at the start of the game).

In the first two equilibria the outcome is that player 1 chooses A and then both players choose C, in the third equilibrium the outcome is that player 1 chooses A and then both players choose D, and in the last equilibrium the outcome is that player 1 chooses B and then both players choose E.

==Questions==
# What is the difference between Multi-stage game and Repeated game?
# Is the total payoff of a multi-stage game a sum of all payoffs of all stage games?
# What is Information Set?
# How is Information Set relevant to Information completeness in extensive-form game.
# Is there an easy way "to solve" Multi-stage game?
# Name the characteristics of a Multi-stage game by S. Tadelis.

==References==
<references />

File:Extensive game with simultaneousmoves.png

2014-02-02T20:31:11Z

Xklit17:

File:Two-stage-game.png

2014-02-02T20:30:54Z

Xklit17: uploaded a new version of "File:Two-stage-game.png"

File:Two-stage-game.png

2014-02-02T20:29:54Z

Xklit17: uploaded a new version of "File:Two-stage-game.png"

Multistage Games

2014-02-02T20:24:23Z

Xklit17:

__TOC__
==Introduction==
[[Normal form|Normal-form games]] models a game where players choose their moves simultaneously without observing other players moves. [[Extensive form|Extensive-form games]] adds a possibility playing sequentially - allowing players to learn about the choices of previous players, so the player can condition his moves based on previous players decisions. [[Extensive form|Extensive-form games]] have their payoff expressed after the end of the game (one "grand game"). In reality, dynamic play over time may be more complex than one game that unfolds over time. Instead, players can play one game that is followed by another, or maybe even several other games.

* Should we consider each game independently, or should we expect players to consider the sequence of different games as one "grand game"?
* How to evaluate total payoffs from a sequence of payoffs in each of the sequentially played stage-games? What is the value of payoff in period ''N'' and in period ''N+20''? If it was just a one-stage-game we could "solve" the game using Weak Perfect Bayesian Equilibrium...
* Will the players moves vary if the stage-game were not played sequentially but as independent games?
* Will a player vary from the stage-game [[Nash equilibrium]] to a different action, which will result him a higher payoff in the following stage-games?

==Definitions==
===Multi-stage game===
A definition of multi-stage game by S. Tadelis is following: A multi-stage game is '''a finite sequence of stage-games''', each one being a game of '''complete but imperfect information''' (a '''simultaneous move game'''). These games are '''played sequentially by the same players''', and the total payoffs from the sequence of games will be evaluated using the sequence of outcomes in the games that were played. We adopt the convention that each game is played in a distinct period, so that game 1 is played in period 1, game 2 in period 2, and so on. We will also assume that after each stage is completed, all the players observe the outcome of that stage, and that this information structure is common knowledge. <ref name="Tadelis2013">Tadelis, Steve. ''Game Theory: An Introduction.'' Princeton: Princeton UP, 2013. Print.</ref>

Multi-stage game consists of multiple games. In each game, players have a set of action they choose from, and the profiles of actions lead to payoffs for that specific game, which is then followed by another game and another, until sequence of games is over. Once we realize that one game follows another, this implies that players can observe the outcomes of each game before another game is played. This observation is important because it allows players to condition their future actions on past outcomes. This is the idea at the center of multi-stage games: the ability to condition behavior may lead to a rich set of outcomes. In what follows, we will analyze the idea of conditional strategies, and the equilibrium that can be supported using such strategies.<ref name="Tadelis2013" />

Other sources use term Multi-stage game with a wider meaning including also games with Perfect Information <ref>Rosu, Ioanid. "Multi-Stage Game Theory in Continous Time." Ioanid Rosu - Research. HEC Paris, 1 Jan. 2006. Web. 2 Feb. 2014.</ref> which is in contrary to the <ref name="Tadelis2013" />. Following material uses definition of S. Tadelis, which is mentioned above.

===Information Set===
[[File:Information-set.png|200px|thumb|right|Information set (dashed blue line)]]
Information Set is collection of decision nodes such that:
* When the play reaches a node in the information set, the player with the move does not know which node in the information set has been reached.
* The player has the same set of choices at each node in the information set.

Information Set can be used in [[Extensive form|extensive-form games]] to view a subgame with simultaneous moves of the players. If the player doesn't have the same set of choices at each node it is not an Information set. The point is that for the player its unknown and undecidable know at what node we are. Why is Information Set used? Because it allows us to view a complicated multi-stage game in a familiar tree view, which is also used in Dynamic Games.

==Conditional strategies==
If a multistage game consists of N games and we break up the games into N individual games and take it as an individual game. And if the players won't try to link them in any way, then the strategies would be pretty simple - each game is treated independently and each player chooses its best strategy to get the highest payoff in the respective stage game.

But in case of a multi-stage game players may want to link the individual games and create a strategy that will yield the best payoff. A simple example of linking different games can be following - If you play a game of chess with me now, I'll go with you to a cinema. If not, I won't go with you. Which generally means using strategies in form of "if A happens in games 1,2... n-1 then I will choose this action in game N". A simple way to explain conditional strategies is to take one of the below examples and write all extensive forms of strategies - "I will play F in the first game and I will play L in the second game only if player 2 played M in the first game. If player 2 played F in the first game then I will play G in the second."

To decide which Strategy would be the best to play for both of the players - similar to finding equilibrium like [[Nash equilibrium]], we would have to introduce Sequential Equilibrium. <ref>David M. Kreps and Robert Wilson. ''Sequential Equilibria'', Econometrica 50:863-894, 1982.</ref> Sequential Equilibrium does specify a strategy for each player and a belief for each of the players. A belief gives, for each information set of the game belonging to the player, a probability distribution on nodes in the information set (see [[Bayesian Equilibrium]]).

==Payoffs==
How to evaluate total payoffs from all of the N stage-games? Is it a simple sum of all of the payoffs from all the stage-games? There is a well defined notion from economic analysis (and standard cost-benefit analysis) of present value which should be used to calculate the total payoff. <ref name="Tadelis2013" />

It is easy to justify the assumption that payoffs obtained in earlier stage-game are worth more than payoffs obtained in later stage-games. Take in consideration financial markets - if a game played today yield a payment of 20 and another is played in a year and it will also yield 20, then today's value of the second payment will be worth less than 20. Say there is a 10% interest rate at which we can borrow money then we can borrow 20 today and repay 22 in a year, which is the future payoff from the game. So the 22 next year is worth exactly 20 today. Alternatively you can use analogy with discount, which you should be definitely familiar with. Another way to justify the assumption of discounting, or ''impatience'', is that today's game is played now and its not 100% certain that the next will be played. For example if two players are playing a game in period one, there may be some probability that tomorrow's game won't be played. Then the payoff of the first game is more reliable and has a higher momentary value independent from the occurrence of the second game, because you have to take in account the probability of not-playing the game, ergo not getting the money.

For more detailed information about calculating the Total Payoff using discounted sum of payoffs that the player expects to get in the sequence of all stage-games see the <ref name="Tadelis2013" />. But the idea is pretty simple - The payoffs in one period away are discounted once, two periods away are discounted twice and so on.

==Subgame Perfect Equilibria==
[[File:Two-stage-game.png|400px|thumb|right]]
Since multi-stage games are dynamic in nature, and the past play is revealed over time, it is natural to turn to Subgame Perfect Equilibrium (SPE) as a solution concept. In particular, rational players should play sequentially rational strategies, which justifies the concept of SPE, and because total payoffs are defined above we are able to use it. Example of a simple two-stage game of two players from <ref name="Tadelis2013" /> is shown on the side, number of possible pure strategies is 32x32 = 1024! If we cannot relay on playing sequentially rational strategies we should turn to the Sequential Equilibrium mentioned above.

==Questions==
# What is the difference between Multi-stage game and Repeated game?
# Is the total payoff of a multi-stage game a sum of all payoffs of all stage games?
# What is Information Set?
# How is Information Set relevant to Information completeness in extensive-form game.
# Is there an easy way "to solve" Multi-stage game?
# Name the characteristics of a Multi-stage game by S. Tadelis.

==References==
<references />

File:Two-stage-game.png

2014-02-02T20:05:58Z

Xklit17:

Multistage Games

2014-02-02T19:54:00Z

Xklit17:

__TOC__
==Introduction==
[[Normal form|Normal-form games]] models a game where players choose their moves simultaneously without observing other players moves. [[Extensive form|Extensive-form games]] adds a possibility playing sequentially - allowing players to learn about the choices of previous players, so the player can condition his moves based on previous players decisions. [[Extensive form|Extensive-form games]] have their payoff expressed after the end of the game (one "grand game"). In reality, dynamic play over time may be more complex than one game that unfolds over time. Instead, players can play one game that is followed by another, or maybe even several other games.

* Should we consider each game independently, or should we expect players to consider the sequence of different games as one "grand game"?
* How to evaluate total payoffs from a sequence of payoffs in each of the sequentially played stage-games? What is the value of payoff in period ''N'' and in period ''N+20''? If it was just a one-stage-game we could "solve" the game using Weak Perfect Bayesian Equilibrium...
* Will the players moves vary if the stage-game were not played sequentially but as independent games?
* Will a player vary from the stage-game [[Nash equilibrium]] to a different action, which will result him a higher payoff in the following stage-games?

==Definitions==
===Multi-stage game===
A definition of multi-stage game by S. Tadelis is following: A multi-stage game is '''a finite sequence of stage-games''', each one being a game of '''complete but imperfect information''' (a '''simultaneous move game'''). These games are '''played sequentially by the same players''', and the total payoffs from the sequence of games will be evaluated using the sequence of outcomes in the games that were played. We adopt the convention that each game is played in a distinct period, so that game 1 is played in period 1, game 2 in period 2, and so on. We will also assume that after each stage is completed, all the players observe the outcome of that stage, and that this information structure is common knowledge. <ref name="Tadelis2013">Tadelis, Steve. ''Game Theory: An Introduction.'' Princeton: Princeton UP, 2013. Print.</ref>

Multi-stage game consists of multiple games. In each game, players have a set of action they choose from, and the profiles of actions lead to payoffs for that specific game, which is then followed by another game and another, until sequence of games is over. Once we realize that one game follows another, this implies that players can observe the outcomes of each game before another game is played. This observation is important because it allows players to condition their future actions on past outcomes. This is the idea at the center of multi-stage games: the ability to condition behavior may lead to a rich set of outcomes. In what follows, we will analyze the idea of conditional strategies, and the equilibrium that can be supported using such strategies.<ref name="Tadelis2013" />

Other sources use term Multi-stage game with a wider meaning including also games with Perfect Information <ref>Rosu, Ioanid. "Multi-Stage Game Theory in Continous Time." Ioanid Rosu - Research. HEC Paris, 1 Jan. 2006. Web. 2 Feb. 2014.</ref> which is in contrary to the <ref name="Tadelis2013" />. Following material uses definition of S. Tadelis, which is mentioned above.

===Information Set===
[[File:Information-set.png|200px|thumb|right|Information set (dashed blue line)]]
Information Set is collection of decision nodes such that:
* When the play reaches a node in the information set, the player with the move does not know which node in the information set has been reached.
* The player has the same set of choices at each node in the information set.

Information Set can be used in [[Extensive form|extensive-form games]] to view a subgame with simultaneous moves of the players. If the player doesn't have the same set of choices at each node it is not an Information set. The point is that for the player its unknown and undecidable know at what node we are. Why is Information Set used? Because it allows us to view a complicated multi-stage game in a familiar tree view, which is also used in Dynamic Games.

==Real Applications==
===Conditional strategies===
If a multistage game consists of N games and we break up the games into N individual games and take it as an individual game. And if the players won't try to link them in any way, then the strategies would be pretty simple - each game is treated independently and each player chooses its best strategy to get the highest payoff in the respective stage game.

But in case of a multi-stage game players may want to link the individual games and create a strategy that will yield the best payoff. A simple example of linking different games can be following - If you play a game of chess with me now, I'll go with you to a cinema. If not, I won't go with you. Which generally means using strategies in form of "if A happens in games 1,2... n-1 then I will choose this action in game N". A simple way to explain conditional strategies is to take one of the below examples and write all extensive forms of strategies - "I will play F in the first game and I will play L in the second game only if player 2 played M in the first game. If player 2 played F in the first game then I will play G in the second."

To decide which Strategy would be the best to play for both of the players - similar to finding equilibrium like [[Nash equilibrium]], we would have to introduce Sequential Equilibrium. <ref>David M. Kreps and Robert Wilson. ''Sequential Equilibria'', Econometrica 50:863-894, 1982.</ref> Sequential Equilibrium does specify a strategy for each player and a belief for each of the players. A belief gives, for each information set of the game belonging to the player, a probability distribution on nodes in the information set (see [[Bayesian Equilibrium]]).

===Payoffs===
How to evaluate total payoffs from all of the N stage-games? Is it a simple sum of all of the payoffs from all the stage-games? There is a well defined notion from economic analysis (and standard cost-benefit analysis) of present value which should be used to calculate the total payoff. <ref name="Tadelis2013" />

It is easy to justify the assumption that payoffs obtained in earlier stage-game are worth more than payoffs obtained in later stage-games. Take in consideration financial markets - if a game played today yield a payment of 20 and another is played in a year and it will also yield 20, then today's value of the second payment will be worth less than 20. Say there is a 10% interest rate at which we can borrow money then we can borrow 20 today and repay 22 in a year, which is the future payoff from the game. So the 22 next year is worth exactly 20 today. Alternatively you can use analogy with discount, which you should be definitely familiar with. Another way to justify the assumption of discounting, or ''impatience'', is that today's game is played now and its not 100% certain that the next will be played. For example if two players are playing a game in period one, there may be some probability that tomorrow's game won't be played. Then the payoff of the first game is more reliable and has a higher momentary value independent from the occurrence of the second game, because you have to take in account the probability of not-playing the game, ergo not getting the money.

==Relevant facts==
(how the phenomenon is used, etc.)

==Interesting things, curiosities==

==Exercises==
that students could use to practice the problem and that could be an inspiration for test questions

==References==
<references />

Multistage Games

2014-02-02T18:07:27Z

Xklit17:

File:Information-set.png

2014-02-02T17:45:10Z

Xklit17:

Multistage Games

2014-02-02T17:23:32Z

Xklit17:

Multistage Games

2014-02-02T16:29:01Z

Xklit17:

Multistage Games

2014-02-02T16:28:46Z

Xklit17:

Multistage Games

2014-02-02T14:36:42Z

Xklit17: Created page with "__TOC__ ==Introduction== ==Definition== <ref> test alskjfalkds jfalsdf jasldkfj asdlfj</ref> ==Real applications== ==Solved example== (more examples are better; one simple, ..."

__TOC__
==Introduction==

==Definition==
<ref> test alskjfalkds jfalsdf jasldkfj asdlfj</ref>
==Real applications==

==Solved example==
(more examples are better; one simple, others more advanced)

==Relevant facts==
(how the phenomenon is used, etc.)

==Interesting things, curiosities==

==Exercises==
that students could use to practice the problem and that could be an inspiration for test questions

==References==
<references />

WS 2013/2014

2014-01-15T22:54:22Z

Xklit17:

Semestral papers from winter term 2013/2014. Please, put here links to the pages with your paper. First you need to have your [[Assignments WS 2013/2014|assignment approved]].

-- [[User:Xziny00|Xziny00]] 20:11, 12 January 2014 (CET) [[Current account opening process optimization]]

-- [[User:Xklit17|Xklit17]] 00:02, 14 January 2014 (CET) [[Intersection (vs. Roundabout)|Intersection (vs. Roundabout)]]

-- [[User:Xvism00|Xvism00]] 13:22, 14 January 2014 (CET)[[General Behavior of Infections]]

-- [[User:Xvott00|Xvott00]] 23:15, 14 January 2014 (CET) [[Fire evacuation simulation]]

-- [[User:Xpeka00|Xpeka00]] 23:54, 14 January 2014 (CET) [[From Field to Forest]]

-- [[User:Xzruv00|Xzruv00]] 18:21, 15 January 2014 (CET) [[Fertility vs Intelligence]]

-- [[User:Xlizt00|Xlizt00]] 19:49, 15 January 2014 (CET) [[Water flow through Vltava water cascade]]

--[[User:Spiglnigl|Spiglnigl]] 22:06, 15 January 2014 (CET) xmalf00 [[Heat recuperation]]

Intersection (vs. Roundabout)

2014-01-15T22:53:49Z

Xklit17:

= Introduction =

= Problem definition =

During the last year almost every day I go around an intersection at Střelnická / Třebenická which has a really unique shape which reminds me of a Roundabout. I'd like to try to simulate the Intersection as an agent based simulation. There are 4 exits from the road:
- to Kaufland (biggest local shop, about 130 parking places)
- to Ďáblický hřbitov and local housing estate
- to Kobylisy
- to Střížkov
On every exit there are traffic lights with different timings, which I'll easily measure during one measurement at one specific time and day of the week. Most of the cars go straight on the main road from Kobylisy to Střížkov, they also arrive mostly at higher speeds than others leaving from the housing estate and Kaufland. I'd like to propose a simulation based model from NetLogo library with an intersection with 4 exists as is the real example. It will allow users to set frequency, deceleration, acceleration of cars from each direction. The lights will be set to constant ticks which will try to simulate the real scenario. I will omit the fact that cars entering the Kaufland parking place have to leave it also, it will behave as a normal street.
Then I'd like to try out a simplified model of Roundabout with the same parameters to compare which of these are better. The simulation would consider some safe distance before another car can enter the roundabout and will have same settings and parameters as intersection. Theoretically I'd love to have two models in one NetLogo project, but I'm yet unsure whether its possible.

== Real data ==
Real measured and approximated frequency of incomming cars are following:
- northbound - 6
- westbound - 48
- southbound - 6
- eastbound - 54

Real lights timings measured and approximated are following:
- north-south - 10s
- east-west - 30s
- yellow - 3s

= Method =
The model requires cars entering at different locations, speeds, exiting at different exits and being autonomous in the defined space and environment. The modeling tool should be able to take in account all these facts, so a agent based simulation seems like a clear choice. The other choice could be SimProcess with defined throughputs of each sub-intersection et cetera, but NetLogo is more suited for this kind of modeling and is way more intuitive and the model is almost self-explanatory.

= Model =
[[File:Xklit17-scheme.png|200px|thumb|right]]
The intersection was simplified to allow easier modeling in NetLogo. The limitations of the model are written in following chapter. The NetLogo world size was set to {{-15,..,15},{-15,..,15}} and in the middle of the model is the intersection. Cars are entering from 4 sides and can exit at any side. All roads were modeled as dual ways as it is in reality, but the cars are unable to change lanes.

The model itself is based on a model Traffic Intersection by U. Wilensky, but it was vastly extended to suit the simulation needs. But the basic settings and description can be found in the base model Traffic Intersection and also in model Info in the NetLogo file.

Although the description and proposal was stating that I'd love to compare this intersection to a roundabout, I was unable to trustworthy simulate the behavior on a roundabout. But in the model there is a scenario that the intersection's lights are down and are all green at once. The cars behavior with lights off is exactly the same as if the lights were on, which is a highly unlikely behavior, because most of the drivers do slow down when they see a problem with lights - e.g. blinking yellow light. Car can turn right (first sub-intersection of the intersection) or left at any sub-intersection, as is complaint with Czech driving laws.

The lights are timed and synchronized in two directions (without priority) to east-west and north-south.
The exit direction of each car is generated based on the set probability settings in the model. For exact algorithm see the sub make-new-cars-sub.
It can be and on default is disallowed to turn by 180 in the intersection and exit at the incoming direction, because of the model settings limitations which doesn't allow explicitly setting this scenario. If it is allowed there is a high chance in the default scenario that the car will use it with 40% to turn around - this behavior was not perceived during observation.

== Limitations ==
- Crossing and related lights timing was omitted.
- The right turning lane in west-east direction was omitted.
- South exit behaves just like another normal road, it doesn't take in consideration that all the cars exiting in this direction have to exit the same, because it leads only to a parking.
- Cars cannot change their lane if they see the other one is more free.
- Cars enter the intersection even though it seems full and jammed.
- The roundabout was simulated really simply - just by having the lights dead.

= Results =
[[File:xklit17-Real-sim.png|200px|thumb|right]]
1. The simulation with real measured data is suitable and work in a similar way as the real intersection, except the limitations noted in previous chapter. As we can see the on the screen-shot from NetLogo after over 15 000 ticks the intersection is not jammed and the incoming and outgoing cars from each direction quite represents the reality.

2. If you set the green lights timings without a correlation with the frequency of incoming cars from respective directions, you can see that the intersection jams. If the frequency of incoming cars from each direction was changing rapidly in time, the light timings would have to be adjusted to mitigate the risk of jams.

3. If you kill the lights (dead-lights switch to ON position) you can see that the waiting time of cars from any direction is almost zero and it allows most cars to go through intersection almost without stopping. But I think it is a flaw of the model, because in real-life scenario with lights dead most of the drivers would slow down and some of them could panic which would lead to random stops and maybe even some accidents. Although the simulation propose that if the intersection was converted to a roundabout, it could be more effective (in terms of waiting time of cars). A specific and rigorous simulation would have to be performed to validate this theory.

= Conclusion =

The problem was to simulate and indicate if it would be better to turn this intersection to a roundabout. The model suggests that the roundabout could be more effective, but the drivers behavior was not simulated properly so it would require more detailed and more complex study. This this simulation vastly extends the current models in NetLogo because it added turning, exiting at different locations, dualways and few other ideas.

= Citations =
Wilensky, U. (1998). NetLogo Traffic Intersection model. http://ccl.northwestern.edu/netlogo/models/TrafficIntersection. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

= Code =
Model source code [[File:xklit17.nlogo]]

Intersection (vs. Roundabout)

2014-01-15T22:53:29Z

Xklit17:

= Introduction =

= Problem definition =

During the last year almost every day I go around an intersection at Střelnická / Třebenická which has a really unique shape which reminds me of a Roundabout. I'd like to try to simulate the Intersection as an agent based simulation. There are 4 exits from the road:
- to Kaufland (biggest local shop, about 130 parking places)
- to Ďáblický hřbitov and local housing estate
- to Kobylisy
- to Střížkov
On every exit there are traffic lights with different timings, which I'll easily measure during one measurement at one specific time and day of the week. Most of the cars go straight on the main road from Kobylisy to Střížkov, they also arrive mostly at higher speeds than others leaving from the housing estate and Kaufland. I'd like to propose a simulation based model from NetLogo library with an intersection with 4 exists as is the real example. It will allow users to set frequency, deceleration, acceleration of cars from each direction. The lights will be set to constant ticks which will try to simulate the real scenario. I will omit the fact that cars entering the Kaufland parking place have to leave it also, it will behave as a normal street.
Then I'd like to try out a simplified model of Roundabout with the same parameters to compare which of these are better. The simulation would consider some safe distance before another car can enter the roundabout and will have same settings and parameters as intersection. Theoretically I'd love to have two models in one NetLogo project, but I'm yet unsure whether its possible.

== Real data ==
Real measured and approximated frequency of incomming cars are following:
- northbound - 6
- westbound - 48
- southbound - 6
- eastbound - 54

Real lights timings measured and approximated are following:
- north-south - 10s
- east-west - 30s
- yellow - 3s

= Method =
The model requires cars entering at different locations, speeds, exiting at different exits and being autonomous in the defined space and environment. The modeling tool should be able to take in account all these facts, so a agent based simulation seems like a clear choice. The other choice could be SimProcess with defined throughputs of each sub-intersection et cetera, but NetLogo is more suited for this kind of modeling and is way more intuitive and the model is almost self-explanatory.

= Model =
[[File:Xklit17-scheme.png|200px|thumb|right]]
The intersection was simplified to allow easier modeling in NetLogo. The limitations of the model are written in following chapter. The NetLogo world size was set to {{-15,..,15},{-15,..,15}} and in the middle of the model is the intersection. Cars are entering from 4 sides and can exit at any side. All roads were modeled as dual ways as it is in reality, but the cars are unable to change lanes.

The model itself is based on a model Traffic Intersection by U. Wilensky, but it was vastly extended to suit the simulation needs. But the basic settings and description can be found in the base model Traffic Intersection and also in model Info in the NetLogo file.

Although the description and proposal was stating that I'd love to compare this intersection to a roundabout, I was unable to trustworthy simulate the behavior on a roundabout. But in the model there is a scenario that the intersection's lights are down and are all green at once. The cars behavior with lights off is exactly the same as if the lights were on, which is a highly unlikely behavior, because most of the drivers do slow down when they see a problem with lights - e.g. blinking yellow light. Car can turn right (first sub-intersection of the intersection) or left at any sub-intersection, as is complaint with Czech driving laws.

The lights are timed and synchronized in two directions (without priority) to east-west and north-south.
The exit direction of each car is generated based on the set probability settings in the model. For exact algorithm see the sub make-new-cars-sub.
It can be and on default is disallowed to turn by 180 in the intersection and exit at the incoming direction, because of the model settings limitations which doesn't allow explicitly setting this scenario. If it is allowed there is a high chance in the default scenario that the car will use it with 40% to turn around - this behavior was not perceived during observation.

== Limitations ==
- Crossing and related lights timing was omitted.
- The right turning lane in west-east direction was omitted.
- South exit behaves just like another normal road, it doesn't take in consideration that all the cars exiting in this direction have to exit the same, because it leads only to a parking.
- Cars cannot change their lane if they see the other one is more free.
- Cars enter the intersection even though it seems full and jammed.
- The roundabout was simulated really simply - just by having the lights dead.

= Results =
[[File:xklit17-Real-sim.png|200px|thumb|right]]
1. The simulation with real measured data is suitable and work in a similar way as the real intersection, except the limitations noted in previous chapter. As we can see the on the screen-shot from NetLogo after over 15 000 ticks the intersection is not jammed and the incoming and outgoing cars from each direction quite represents the reality.
2. If you set the green lights timings without a correlation with the frequency of incoming cars from respective directions, you can see that the intersection jams. If the frequency of incoming cars from each direction was changing rapidly in time, the light timings would have to be adjusted to mitigate the risk of jams.
3. If you kill the lights (dead-lights switch to ON position) you can see that the waiting time of cars from any direction is almost zero and it allows most cars to go through intersection almost without stopping. But I think it is a flaw of the model, because in real-life scenario with lights dead most of the drivers would slow down and some of them could panic which would lead to random stops and maybe even some accidents. Although the simulation propose that if the intersection was converted to a roundabout, it could be more effective (in terms of waiting time of cars). A specific and rigorous simulation would have to be performed to validate this theory.

= Conclusion =

The problem was to simulate and indicate if it would be better to turn this intersection to a roundabout. The model suggests that the roundabout could be more effective, but the drivers behavior was not simulated properly so it would require more detailed and more complex study. This this simulation vastly extends the current models in NetLogo because it added turning, exiting at different locations, dualways and few other ideas.

= Citations =
Wilensky, U. (1998). NetLogo Traffic Intersection model. http://ccl.northwestern.edu/netlogo/models/TrafficIntersection. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

= Code =
Model source code [[File:xklit17.nlogo]]

File:Xklit17-Real-sim.png

2014-01-15T22:52:59Z

Xklit17:

Intersection (vs. Roundabout)

2014-01-15T22:52:25Z

Xklit17:

= Introduction =

= Problem definition =

During the last year almost every day I go around an intersection at Střelnická / Třebenická which has a really unique shape which reminds me of a Roundabout. I'd like to try to simulate the Intersection as an agent based simulation. There are 4 exits from the road:
- to Kaufland (biggest local shop, about 130 parking places)
- to Ďáblický hřbitov and local housing estate
- to Kobylisy
- to Střížkov
On every exit there are traffic lights with different timings, which I'll easily measure during one measurement at one specific time and day of the week. Most of the cars go straight on the main road from Kobylisy to Střížkov, they also arrive mostly at higher speeds than others leaving from the housing estate and Kaufland. I'd like to propose a simulation based model from NetLogo library with an intersection with 4 exists as is the real example. It will allow users to set frequency, deceleration, acceleration of cars from each direction. The lights will be set to constant ticks which will try to simulate the real scenario. I will omit the fact that cars entering the Kaufland parking place have to leave it also, it will behave as a normal street.
Then I'd like to try out a simplified model of Roundabout with the same parameters to compare which of these are better. The simulation would consider some safe distance before another car can enter the roundabout and will have same settings and parameters as intersection. Theoretically I'd love to have two models in one NetLogo project, but I'm yet unsure whether its possible.

== Real data ==
Real measured and approximated frequency of incomming cars are following:
- northbound - 6
- westbound - 48
- southbound - 6
- eastbound - 54

Real lights timings measured and approximated are following:
- north-south - 10s
- east-west - 30s
- yellow - 3s

= Method =
The model requires cars entering at different locations, speeds, exiting at different exits and being autonomous in the defined space and environment. The modeling tool should be able to take in account all these facts, so a agent based simulation seems like a clear choice. The other choice could be SimProcess with defined throughputs of each sub-intersection et cetera, but NetLogo is more suited for this kind of modeling and is way more intuitive and the model is almost self-explanatory.

= Model =
[[File:Xklit17-scheme.png|200px|thumb|right]]
The intersection was simplified to allow easier modeling in NetLogo. The limitations of the model are written in following chapter. The NetLogo world size was set to {{-15,..,15},{-15,..,15}} and in the middle of the model is the intersection. Cars are entering from 4 sides and can exit at any side. All roads were modeled as dual ways as it is in reality, but the cars are unable to change lanes.

The model itself is based on a model Traffic Intersection by U. Wilensky, but it was vastly extended to suit the simulation needs. But the basic settings and description can be found in the base model Traffic Intersection and also in model Info in the NetLogo file.

Although the description and proposal was stating that I'd love to compare this intersection to a roundabout, I was unable to trustworthy simulate the behavior on a roundabout. But in the model there is a scenario that the intersection's lights are down and are all green at once. The cars behavior with lights off is exactly the same as if the lights were on, which is a highly unlikely behavior, because most of the drivers do slow down when they see a problem with lights - e.g. blinking yellow light. Car can turn right (first sub-intersection of the intersection) or left at any sub-intersection, as is complaint with Czech driving laws.

The lights are timed and synchronized in two directions (without priority) to east-west and north-south.
The exit direction of each car is generated based on the set probability settings in the model. For exact algorithm see the sub make-new-cars-sub.
It can be and on default is disallowed to turn by 180 in the intersection and exit at the incoming direction, because of the model settings limitations which doesn't allow explicitly setting this scenario. If it is allowed there is a high chance in the default scenario that the car will use it with 40% to turn around - this behavior was not perceived during observation.

== Limitations ==
- Crossing and related lights timing was omitted.
- The right turning lane in west-east direction was omitted.
- South exit behaves just like another normal road, it doesn't take in consideration that all the cars exiting in this direction have to exit the same, because it leads only to a parking.
- Cars cannot change their lane if they see the other one is more free.
- Cars enter the intersection even though it seems full and jammed.
- The roundabout was simulated really simply - just by having the lights dead.

= Results =
1. The simulation with real measured data is suitable and work in a similar way as the real intersection, except the limitations noted in previous chapter. As we can see the on the screen-shot from NetLogo after over 15 000 ticks the intersection is not jammed and the incoming and outgoing cars from each direction quite represents the reality.
2. If you set the green lights timings without a correlation with the frequency of incoming cars from respective directions, you can see that the intersection jams. If the frequency of incoming cars from each direction was changing rapidly in time, the light timings would have to be adjusted to mitigate the risk of jams.
3. If you kill the lights (dead-lights switch to ON position) you can see that the waiting time of cars from any direction is almost zero and it allows most cars to go through intersection almost without stopping. But I think it is a flaw of the model, because in real-life scenario with lights dead most of the drivers would slow down and some of them could panic which would lead to random stops and maybe even some accidents. Although the simulation propose that if the intersection was converted to a roundabout, it could be more effective (in terms of waiting time of cars). A specific and rigorous simulation would have to be performed to validate this theory.

= Conclusion =

The problem was to simulate and indicate if it would be better to turn this intersection to a roundabout. The model suggests that the roundabout could be more effective, but the drivers behavior was not simulated properly so it would require more detailed and more complex study. This this simulation vastly extends the current models in NetLogo because it added turning, exiting at different locations, dualways and few other ideas.

= Citations =
Wilensky, U. (1998). NetLogo Traffic Intersection model. http://ccl.northwestern.edu/netlogo/models/TrafficIntersection. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

= Code =
Model source code [[File:xklit17.nlogo]]

File:Xklit17.nlogo

2014-01-15T22:50:39Z

Xklit17: uploaded a new version of "File:Xklit17.nlogo"

Intersection (vs. Roundabout)

2014-01-15T22:34:50Z

Xklit17: finalization

= Introduction =

= Problem definition =

During the last year almost every day I go around an intersection at Střelnická / Třebenická which has a really unique shape which reminds me of a Roundabout. I'd like to try to simulate the Intersection as an agent based simulation. There are 4 exits from the road:
- to Kaufland (biggest local shop, about 130 parking places)
- to Ďáblický hřbitov and local housing estate
- to Kobylisy
- to Střížkov
On every exit there are traffic lights with different timings, which I'll easily measure during one measurement at one specific time and day of the week. Most of the cars go straight on the main road from Kobylisy to Střížkov, they also arrive mostly at higher speeds than others leaving from the housing estate and Kaufland. I'd like to propose a simulation based model from NetLogo library with an intersection with 4 exists as is the real example. It will allow users to set frequency, deceleration, acceleration of cars from each direction. The lights will be set to constant ticks which will try to simulate the real scenario. I will omit the fact that cars entering the Kaufland parking place have to leave it also, it will behave as a normal street.
Then I'd like to try out a simplified model of Roundabout with the same parameters to compare which of these are better. The simulation would consider some safe distance before another car can enter the roundabout and will have same settings and parameters as intersection. Theoretically I'd love to have two models in one NetLogo project, but I'm yet unsure whether its possible.

== Real data ==
Real measured and approximated frequency of incomming cars are following:
- northbound - 6
- westbound - 48
- southbound - 6
- eastbound - 54

Real lights timings measured and approximated are following:
- north-south - 10s
- east-west - 30s
- yellow - 3s

= Method =
The model requires cars entering at different locations, speeds, exiting at different exits and being autonomous in the defined space and environment. The modeling tool should be able to take in account all these facts, so a agent based simulation seems like a clear choice. The other choice could be SimProcess with defined throughputs of each sub-intersection et cetera, but NetLogo is more suited for this kind of modeling and is way more intuitive and the model is almost self-explanatory.

= Model =
[[File:Xklit17-scheme.png|200px|thumb|right]]
The intersection was simplified to allow easier modeling in NetLogo. The limitations of the model are written in following chapter. The NetLogo world size was set to {{-15,..,15},{-15,..,15}} and in the middle of the model is the intersection. Cars are entering from 4 sides and can exit at any side. All roads were modeled as dual ways as it is in reality, but the cars are unable to change lanes.

The model itself is based on a model Traffic Intersection by U. Wilensky, but it was vastly extended to suit the simulation needs. But the basic settings and description can be found in the base model Traffic Intersection and also in model Info in the NetLogo file.

Although the description and proposal was stating that I'd love to compare this intersection to a roundabout, I was unable to trustworthy simulate the behavior on a roundabout. But in the model there is a scenario that the intersection's lights are down and are all green at once. The cars behavior with lights off is exactly the same as if the lights were on, which is a highly unlikely behavior, because most of the drivers do slow down when they see a problem with lights - e.g. blinking yellow light.

The lights are timed and synchronized in two directions (without priority) to east-west and north-south.
The exit direction of each car is generated based on the set probability settings in the model. For exact algorithm see the sub make-new-cars-sub.
It can be and on default is disallowed to turn by 180 in the intersection and exit at the incoming direction, because of the model settings limitations which doesn't allow explicitly setting this scenario. If it is allowed there is a high chance in the default scenario that the car will use it with 40% to turn around - this behavior was not perceived during observation.

== Limitations ==
- Crossing and related lights timing was omitted.
- The right turning lane in west-east direction was omitted.
- South exit behaves just like another normal road, it doesn't take in consideration that all the cars exiting in this direction have to exit the same, because it leads only to a parking.
- Cars cannot change their lane if they see the other one is more free.
- Cars enter the intersection even though it seems full and jammed.
- The roundabout was simulated really simply - just by having the lights dead.

= Results =
1. The simulation with real measured data is suitable and work in a similar way as the real intersection, except the limitations noted in previous chapter. As we can see the on the screen-shot from NetLogo after over 15 000 ticks the intersection is not jammed and the incoming and outgoing cars from each direction quite represents the reality.
2. If you set the green lights timings without a correlation with the frequency of incoming cars from respective directions, you can see that the intersection jams. If the frequency of incoming cars from each direction was changing rapidly in time, the light timings would have to be adjusted to mitigate the risk of jams.
3. If you kill the lights (dead-lights switch to ON position) you can see that the waiting time of cars from any direction is almost zero and it allows most cars to go through intersection almost without stopping. But I think it is a flaw of the model, because in real-life scenario with lights dead most of the drivers would slow down and some of them could panic which would lead to random stops and maybe even some accidents. Although the simulation propose that if the intersection was converted to a roundabout, it could be more effective (in terms of waiting time of cars). A specific and rigorous simulation would have to be performed to validate this theory.

= Conclusion =

The problem was to simulate and indicate if it would be better to turn this intersection to a roundabout. The model suggests that the roundabout could be more effective, but the drivers behavior was not simulated properly so it would require more detailed and more complex study. This this simulation vastly extends the current models in NetLogo because it added turning, exiting at different locations, dualways and few other ideas.

= Citations =
Wilensky, U. (1998). NetLogo Traffic Intersection model. http://ccl.northwestern.edu/netlogo/models/TrafficIntersection. Center for Connected Learning and Computer-Based Modeling, Northwestern Institute on Complex Systems, Northwestern University, Evanston, IL.

= Code =
Model source code [[File:xklit17.nlogo]]

File:Xklit17.nlogo

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File:Xklit17-scheme.png

2014-01-15T21:40:37Z

Xklit17:

Intersection (vs. Roundabout)

2014-01-15T21:39:25Z

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Intersection (vs. Roundabout)

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= Introduction =

= Problem definition =

- a description of the situation you solve (i.e. the task)

= Method =

- the discussion of possible solutions, the selection of method and tools for the solution, reasons for such choice (why the selected methods and tools are the best for the problem)

= Model =
Detailed description of the method, including parameters, ranges, schemes, model limitations, etc. The description must be detailed enough that anybody could replicate the experiment event without your model source codes.

= Results =

- list of results, their analysis, interpretation and evaluation.

= Conclusion =

- how the problem was solved

= Citations =

= Code =

Model source code (xls, spm, nlogo, mdl, etc. file)

Intersection (vs. Roundabout)

2014-01-14T09:31:11Z

Xklit17:

== Problem definition ==

- a description of the situation you solve (i.e. the task)

== Method ==

- the discussion of possible solutions, the selection of method and tools for the solution, reasons for such choice (why the selected methods and tools are the best for the problem)

Detailed description of the method, including parameters, ranges, schemes, model limitations, etc. The description must be detailed enough that anybody could replicate the experiment event without your model source codes.

== Results ==

- list of results, their analysis, interpretation and evaluation.

== Conclusion ==

- how the problem was solved

== Citations ==

== Simulation ==

Model source code (xls, spm, nlogo, mdl, etc. file)

Intersection (vs. Roundabout)

2014-01-14T09:30:54Z

Xklit17: Created page with "= Intersection (vs. Roundabout) = == Problem definition == - a description of the situation you solve (i.e. the task) == Method == - the discussion of possible solution..."

= Intersection (vs. Roundabout) =

== Problem definition ==

- a description of the situation you solve (i.e. the task)

== Method ==

- the discussion of possible solutions, the selection of method and tools for the solution, reasons for such choice (why the selected methods and tools are the best for the problem)

Detailed description of the method, including parameters, ranges, schemes, model limitations, etc. The description must be detailed enough that anybody could replicate the experiment event without your model source codes.

== Results ==

- list of results, their analysis, interpretation and evaluation.

== Conclusion ==

- how the problem was solved

== Citations ==

== Simulation ==

Model source code (xls, spm, nlogo, mdl, etc. file)

WS 2013/2014

2014-01-13T23:02:42Z

Xklit17: +intersection vs. roundabout WorkInProgress

Assignments WS 2013/2014

2013-12-10T08:58:17Z

Xklit17:

{{DISPLAYTITLE:Assignments WS 2013/2014}}

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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/en|How to deal with the simulation assignment]].
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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.
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==Fertility and intelligence==
<div>
Demographic studies have indicated that in humans, fertility rate and intelligence tend to be inversely correlated - the more intelligent (measured by IQ tests) a person is, the lower total fertility rate it exhibit. Survival rates are also correlated with IQ. Does this mean, that the humans get dumber than they are now?
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<div>
To relax the problem, lets assume that there is a designed, shared space (capacity) for fertility and IQ. What would be the final ratio between intelligence and fertility?
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<div>
Each agent in the model would have a complementary values for inteligence and for having kids (i.e. iq 0.7, fert 0.3). The agents first search for a life partner (there is a higher probability for the ones with similar iq/fert to became life partners - the fact is related to IQ). After finding one, the probabilities of fertility of both parents will determine if they will have a kid, or kids. If so, the kids will acquire parents' averaged values with some possibility of mutation. What will happen if we populate a hypothetic world with two types of people - the clever ones and the fertile ones. Will there be a minority of the clever people, or will they became extinct? Will there be only one group left with a certain amount of iq (higher IQ than within the fertile group at the beginning but dumber than within the ones from the clever group)?
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<div>
I will use Netlogo. Furthermore, depending on complexity of the problem, I would like to introduce basic features like agent age and general life time events, concept of family, etc...
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<div>
Vojtěch Zrůst, Xzruv00
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==Fire evacuation simulation==
<div>
My intention is to create a model of evacuation process of real public building in case of fire emergency. My model considers people as agents who don’t know the way out and in case of fire, they have to find the way first. For this reason there are green tables on the walls of public buildings that should help people find their way to safety.
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<div>
Agents will have to deal with fire and toxic smoke spreading through building on their way out and also other agents, who could crush them in panic.
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<div>
For simulation I am going to use as environment 2D version of NetLogo 5.0.4.
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<div>
My model will count the time of evacuation process and loses of people and help consider whether the green “Exit” tables are on right places and in right amount.
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<div>
Tomáš Votruba, [[User:Xvott00|Xvott00]] 17:11, 7 December 2013 (CET)
</div>
:Generally, it could be an interesting research. It should incorporate more complex shapes of premises than just rectangle (in our class example). The greatest problem could be the intelligence of simulated people. If it should be realistic, it could be quite tricky to develop. Please, could you describe a little bit more in detail, how people would navigate along the green warning tables? [[User:Tomáš|Tomáš]] 01:58, 8 December 2013 (CET)

<p>
Every agent would have own line of sight dependant on where he is facing and how far can he see. When fire alarm will sound, agents will look around and try to find green table. If he sees one, he goes to it. Every green table shows direction (not strictly in line) to the exit, and agent will go that direction, until he sees another table, which will give him another direction, or exit. Green tables will work as some sort of checkpoints, which will lead the agents to safety.
</p>
<p>
If agent doesn´t see any green table, he will try to look for one by looking around and walking randomly chosen direction.
My intention is to use one floor of real existing public building (for example) Centrum Černý Most or similar. I am not telling which one so far, because I still don´t know whether I get proper plans, I could use. But it will definitely won´t be just a rectangle.
</p>
<p>
Tomáš Votruba, [[User:Xvott00|Xvott00]] 15:37, 8 December 2013 (CET)
</p>

==Simulating and optimizing a process of opening an account at the branch of a bank==
<div>
Currently I am working as a junior process manager at one of the banks in Prague and participating in a Lean Six Sigma project of optimization of an account opening by client visiting a bank`s branch. The goal of that project is to minimize time spent by client at a branch and the number of client`s signatures on various contracts by creating a unified multicontract form.
<ul>
The goal of my simulation, which I`d like to make in SimProcess, is to simulate as-is process and identify, at which steps there is idle time and at which steps there could be a queue of customers. Afterwards I would simulate an improved process - that simulation should prove that the process is improved. The goal of simulation is the same as the goal of the real project that I take part in - it is to cut non-value added steps and reduce time spent by customer at the branch. Simulation will be based on real data.
xziny00 20:16, 1 December 2013 (CET)
</ul>
OK, '''approved''' [[User:Tomáš|Tomáš]] 01:37, 8 December 2013 (CET)

==Political compass==
<div>
I am interested to create a simulation of the political spectrum in the NetLogo. The model would simulate the distribution of political views of hypothetical country and the development of leader´s preferences or political parties that people vote. There would be several variable parameters of the population, population growth, a possible radicalization of society, etc. The model would shows electoral preference at the time on the graph and there would be also moving agents on the graphics part of the model. One tick would correspond to one week. The whole model would therefore ran for four years, which is the standard electoral term. In this time there could occur some populist events that affect the electoral battle (floods, the introduction of direct democracy, etc.)
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<div>
Political compass would be based on the known distribution of the political spectrum into 4 quadrants. The horizontal axis would represent the position of voters and political parties to the "left" and "right". The position on the vertical axis would show whether the voter or political party rather libertarian, or authoritarian opinions. Agents (voters) will change slightly their electoral preference every tick. This would simulate a real reflection of the political situation as caving scandals, bad / good economic performance, etc.
</div>
Tomas Lizner, xlizt00, 00:11, 3 December 2013 (CET)
:If this kind of simulation should be developed, I would think about systems dynamics instead of agent-based simulation. But, first and foremost I am generally not very happy about "soft" topics. It is very hard to measure such things like political attitudes. Often, the risk of similar simulation is that it will be nothing more than an academic exercise. Please, try to reconsider it. [[User:Tomáš|Tomáš]] 01:47, 8 December 2013 (CET)
<div>
OK, I have another idea of the model simulation in NetLogo. It would be a simulation of water flow throuhg Vltava water cascade. The principle of the simulation would be how fast can the individual dams release water without the river was on third flood stage (third flood stage is defined by flowrate). There would be agents: individual dams - they would have attributes such as inflow, outflow, retention, current capacity, the risk of rupturing etc. Between the dams would be used Links that represent the waterway between the dams (attributes: normal flow, current flow, flooding flowrate). These information I am able to find out through the internet.
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There would be randomly generated a rainfall (or constant rain) at the beginning of the simulation and they would have an impact on the water cascade. One tick would correspond to one hour, during which time the water is slowly seeping into the ground itself. User would change sliders to make affect to the rate of outflow for individual dams and also there would be settings for weather. Changes in the running simulation would appear on the graph and in a simplified graphical display. I would use NetLogo, because simulation conditions such as a weather conditions and flowout rates of the individual dams can be changed in real time during the simulation, which makes the simulation more interesting and more relevant to reality.
<div>
<div>
Tomas Lizner, xlizt00, 14:11, 9 December 2013 (CET)
<div>

==From field to forest==
<div>
When a field is left alone it takes quite a time until forest spreads on it; this process is called secondary succession. At first pioneering plants such as grasses and herbaceous plants grow there, later invasive small bushes and trees are following. Later on fast growing evergreen trees appear, but they are overtopped with deciduous trees and the forest starts to appear. I would like to propose a model of this situation focused on the influence of the fertility of the field in the very beginning of the process, i. e. I propose the question how long it takes for a forest to appear based on primary fertility of a field.
</div>
<div>
The process of succession is described well on Wikipedia: [http://en.wikipedia.org/wiki/Ecological_succession#Primary_and_secondary_succession].
</div>
<div>
The simulation will be realized as a NetLogo model.
Agents: herbaceous plants, invasive bushes, evergreen trees, deciduous trees.
Agents parameters: probability of survival to the next year, probability to spread.

Each agent can spread under different conditions, such as plants around (of the same kind and of other kinds as well) and fertility of the ground. Each plant lives for a specific period of time.

The fertility of the field is dependent on plants previously living there and on an initial value set in the model.
</div>
Alice Peková, xpeka00, 7 December 2013
:First, is the fertility of soil the only driver of the process? And second, I don't like that you would work generally with trees, bushes, etc. instead of particular kinds. I guess there are probably substantial differences in parameters (like the speed of growth) between different kinds of trees, aren't they? [[User:Tomáš|Tomáš]] 02:53, 8 December 2013 (CET)

==HIV Infection spread==
<div> The World AIDS Day is observed on the 1st of December, so the most recent one was just a week ago. Everybody knows that HIV virus spread is a serious world-wide problem and a lot of people know how the infection spreads. However, it is extremely hard to predict the future development. </div>
<div>Therefore I would like to simulate the HIV infection spread patterns in NetLogo. The agents in the simulation are people who can be either infected or not. Other parameters of the agents (and different subspecies of the agents) are: the fact whether the agent knows about his condition (important especially with infected patients who would generally consciously avoid more infection spread), sexual orientation, birth control method used. Other very specific parameters such as age, marital status, celibacy, sexual practics used could be also considered. </div>
<div>There are several ways how an individual can become infected. The approximate chances are listed on wikipedia page (http://en.wikipedia.org/wiki/HIV/AIDS#Sexual). The fact that people who know about their condition can behave differently depending on their „level of conscience“ contributes to the complexity of the whole system.
</div>
Lucia Banakova, xbanl00, 9.12.2013

==Intersection (vs. Roundabout)==
During the last year almost every day I go around an intersection at [http://mapy.cz/s/8Wbj Střelnická / Třebenická] which has a really unique shape which reminds me of a Roundabout. I'd like to try to simulate the Intersection as an agent based simulation. There are 4 exits from the road:
- to Kaufland (biggest local shop, about 130 parking places)
- to Ďáblický hřbitov and local housing estate
- to Kobylisy
- to Střížkov
On every exit there are traffic lights with different timings, which I'll easily measure during one measurement at one specific time and day of the week. Most of the cars go straight on the main road from Kobylisy to Střížkov, they also arrive mostly at higher speeds than others leaving from the housing estate and Kaufland. I'd like to propose a simulation based model from NetLogo library with an intersection with 4 exists as is the real example. It will allow users to set frequency, deceleration, acceleration of cars from each direction. The lights will be set to constant ticks which will try to simulate the real scenario. I will omit the fact that cars entering the Kaufland parking place have to leave it also, it will behave as a normal street.

Then I'd like to try out a simplified model of Roundabout with the same parameters to compare which of these are better. The simulation would consider some safe distance before another car can enter the roundabout and will have same settings and parameters as intersection. Theoretically I'd love to have two models in one NetLogo project, but I'm yet unsure whether its possible.

[[User:Xklit17|Xklit17]] 09:58, 10 December 2013 (CET)