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game_theory [2023/02/08 22:59] – [The Prisoner's Dilemma] ronigame_theory [2024/04/12 09:41] (current) – [The Prisoner's Dilemma] tom
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 +{{tag>IEMT Model Framework}} 
 ======Game Theory====== ======Game Theory======
  
-The [[iemt_wiki|IEMT]] model is developed around the model of Zero-Sum Game Theory, particularly with regard to the Five Patterns of Chronicity. Game theory is a mathematical framework for modelling and analysing situations in which decision-makers interact to maximise their own interests. It is used to study decision-making in various fields, such as economics, political science, psychology, and biology. The theory considers the strategic interdependence between players and provides methods for predicting and explaining the outcome of interactions in different types of games, such as cooperative and non-cooperative games. Some of the key concepts in game theory include Nash equilibrium, the prisoner's dilemma, and bargaining solutions.+The [[iemt_wiki|IEMT]] model is developed around the model of Zero-Sum Game Theory, particularly with regard to the [[iemt#patterns_of_chronicity|Five Patterns of Chronicity]]. Game theory[(Game_theory>Game theory[[https://en.wikipedia.org/wiki/Game_theory|Wikipedia]])] is a mathematical framework for modelling and analysing situations in which decision-makers interact to maximise their own interests. It is used to study decision-making in various fields, such as economics, political science, psychology, and biology. The theory considers the strategic interdependence between players and provides methods for predicting and explaining the outcome of interactions in different types of games, such as cooperative and non-cooperative games. Some of the key concepts in game theory include Nash equilibrium, the prisoner's dilemma, and bargaining solutions.
  
  
 ====Nash Equilibrium==== ====Nash Equilibrium====
  
-The Nash Equilibrium is a solution concept in game theory named after mathematician and economist John Nash. It is a situation in which each player in a game has determined the best strategy for themselves based on the strategies chosen by the other players.John Nash was a mathematician and economist who was awarded the Nobel Prize in Economics in 1994 for his work in game theory. He was also known for his battle with schizophrenia, which was depicted in the film "A Beautiful Mind."+The Nash Equilibrium[(Nash_equilibrium>Nash equilibrium[[https://en.wikipedia.org/wiki/Nash_equilibrium|Wikipedia]])] is a solution concept in game theory named after mathematician and economist John Nash. It is a situation in which each player in a game has determined the best strategy for themselves based on the strategies chosen by the other players. John Nash was a mathematician and economist who was awarded the Nobel Prize in Economics in 1994 for his work in game theory. He was also known for his battle with schizophrenia, which was depicted in the film "A Beautiful Mind."
  
 Formally, a Nash Equilibrium is a set of strategies, one for each player, such that no player has an incentive to deviate from their strategy given the strategies of the other players. This means that if all players follow their Nash Equilibrium strategies, the outcome is stable and cannot be improved upon by any single player changing their strategy. Formally, a Nash Equilibrium is a set of strategies, one for each player, such that no player has an incentive to deviate from their strategy given the strategies of the other players. This means that if all players follow their Nash Equilibrium strategies, the outcome is stable and cannot be improved upon by any single player changing their strategy.
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 In real-world situations, Nash Equilibria may not always reflect the socially optimal outcome, as the individual incentives may not align with the social good. In such cases, alternative solution concepts, such as the Pareto efficiency or the Correlated Equilibrium, may provide a more realistic representation of the situation. In real-world situations, Nash Equilibria may not always reflect the socially optimal outcome, as the individual incentives may not align with the social good. In such cases, alternative solution concepts, such as the Pareto efficiency or the Correlated Equilibrium, may provide a more realistic representation of the situation.
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 ====The Pareto Efficiency==== ====The Pareto Efficiency====
  
-The Pareto Efficiency, named after economist Vilfredo Pareto, is a concept in economics that describes a situation in which it is impossible to make any one individual better off without making another individual worse off. In other words, a Pareto efficient outcome is one in which no further improvement can be made without making at least one person worse off. Vilfredo Pareto (1848–1923) was an Italian engineer, sociologist, and economist. He made significant contributions to a wide range of fields, including economics, sociology, and political science.+The Pareto Efficiency[(Pareto_efficiency>Pareto efficiency[[https://en.wikipedia.org/wiki/Pareto_efficiency|Wikipedia]])], named after economist Vilfredo Pareto, is a concept in economics that describes a situation in which it is impossible to make any one individual better off without making another individual worse off. In other words, a Pareto efficient outcome is one in which no further improvement can be made without making at least one person worse off. Vilfredo Pareto (1848–1923) was an Italian engineer, sociologist, and economist. He made significant contributions to a wide range of fields, including economics, sociology, and political science.
  
 The concept of Pareto Efficiency is used to assess the efficiency of economic systems and is often used as a benchmark for determining whether a proposed change will lead to a more efficient outcome. A change that makes one person better off and no one worse off is considered to be a Pareto improvement, while a change that makes one person worse off is considered to be a Pareto regression. The concept of Pareto Efficiency is used to assess the efficiency of economic systems and is often used as a benchmark for determining whether a proposed change will lead to a more efficient outcome. A change that makes one person better off and no one worse off is considered to be a Pareto improvement, while a change that makes one person worse off is considered to be a Pareto regression.
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 ====Correlated Equilibrium==== ====Correlated Equilibrium====
  
-Correlated Equilibrium is a solution concept in game theory that extends the Nash Equilibrium by allowing for randomization or correlation in the strategies of the players. In a Correlated Equilibrium, each player's strategy is determined by a random process that takes into account the strategies of all the players, rather than just the strategies of the other players, as in a Nash Equilibrium.+Correlated Equilibrium[(Correlated_equilibrium>Correlated equilibrium[[https://en.wikipedia.org/wiki/Correlated_equilibrium|Wikipedia]])] is a solution concept in game theory that extends the Nash Equilibrium by allowing for randomization or correlation in the strategies of the players. In a Correlated Equilibrium, each player's strategy is determined by a random process that takes into account the strategies of all the players, rather than just the strategies of the other players, as in a Nash Equilibrium.
  
 The concept of Correlated Equilibrium allows for the possibility of coordination and cooperation between players, as their strategies can be correlated in a way that benefits all players. This makes Correlated Equilibrium a more realistic solution concept in situations where coordination and cooperation are important. The concept of Correlated Equilibrium allows for the possibility of coordination and cooperation between players, as their strategies can be correlated in a way that benefits all players. This makes Correlated Equilibrium a more realistic solution concept in situations where coordination and cooperation are important.
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 ====Rawlsian Fairness Criterion==== ====Rawlsian Fairness Criterion====
  
-The Rawlsian fairness criterion is a solution concept in social and political philosophy that is named after philosopher John Rawls. The Rawlsian fairness criterion is used to evaluate the fairness of a particular outcome or distribution of resources in a society. John Rawls (1921–2002) was an American philosopher and political economist. He is widely regarded as one of the most important political philosophers of the 20th century and is best known for his theory of justice as fairness, which is presented in his seminal work "A Theory of Justice." Rawls believed that a just society is one in which the basic structure of society, including the distribution of resources and opportunities, is arranged to benefit the least advantaged members of society.+The Rawlsian[(Justice_as_Fairness>Justice as Fairness[[https://en.wikipedia.org/wiki/Justice_as_Fairness|Wikipedia]])] fairness criterion is a solution concept in social and political philosophy that is named after philosopher John Rawls. The Rawlsian fairness criterion is used to evaluate the fairness of a particular outcome or distribution of resources in a society. John Rawls (1921–2002) was an American philosopher and political economist. He is widely regarded as one of the most important political philosophers of the 20th century and is best known for his theory of justice as fairness, which is presented in his seminal work "A Theory of Justice." Rawls believed that a just society is one in which the basic structure of society, including the distribution of resources and opportunities, is arranged to benefit the least advantaged members of society.
  
 The Rawlsian fairness criterion is based on two principles of justice: the first, the principle of equal basic liberties, states that everyone is entitled to a set of basic liberties and rights that cannot be taken away; the second,  the difference principle, states that social and economic inequalities are only just if they are to the greatest benefit of the least advantaged. The Rawlsian fairness criterion is based on two principles of justice: the first, the principle of equal basic liberties, states that everyone is entitled to a set of basic liberties and rights that cannot be taken away; the second,  the difference principle, states that social and economic inequalities are only just if they are to the greatest benefit of the least advantaged.
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 =====Zero-Sum Game Theory===== =====Zero-Sum Game Theory=====
  
-Zero-sum game theory is a branch of game theory where the total benefit or gain of all players {{ :zero_sum_game_-_advanced.png?nolink&400|}}in the game is equal to zero. In other words, in a zero-sum game, one player's gain is exactly balanced by the losses of the other players. The concept is based on the idea that the total benefit of a game remains constant and that any gain by one player must come at the expense of another player. +<WRAP 300 RIGHT> 
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 +Zero-sum game[(Zero-sum_game>Zero-sum game[[https://en.wikipedia.org/wiki/Zero-sum_game|Wikipedia]])] 
 + theory is a branch of game theory where the total benefit or gain of all players in the game is equal to zero. In other words, in a zero-sum game, one player's gain is exactly balanced by the losses of the other players. The concept is based on the idea that the total benefit of a game remains constant and that any gain by one player must come at the expense of another player.
 Examples of zero-sum games include chess, poker, and rock-paper-scissors. In these games, one player's win results in the loss of the other player, and the total winnings and losses balance out to zero. In poker, for instance, if one player wins a hand, the other players must have lost that same amount. Examples of zero-sum games include chess, poker, and rock-paper-scissors. In these games, one player's win results in the loss of the other player, and the total winnings and losses balance out to zero. In poker, for instance, if one player wins a hand, the other players must have lost that same amount.
  
 In contrast, non-zero-sum games, such as many real-world economic and political interactions, do not have a constant total benefit. In these games, the actions of one player can increase the total benefit for all players, such as in a cooperative game where players work together to achieve a common goal. In contrast, non-zero-sum games, such as many real-world economic and political interactions, do not have a constant total benefit. In these games, the actions of one player can increase the total benefit for all players, such as in a cooperative game where players work together to achieve a common goal.
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 +The more participants viewed social hierarchies as zero-sum, the more they were willing to use dominance tactics...zero-sum beliefs about hierarchies increase the preference for dominance-oriented, but not prestige-oriented, strategies for gaining rank
 +<cite>Is status a zero-sum game? [(APA>Is status a zero-sum game? Zero-sum beliefs increase people’s preference for dominance but not prestige.[[https://psycnet.apa.org/doiLanding?doi=10.1037%2Fxge0001282|psycnet.apa.org]])]
 +</cite>
 +</blockquote>
  
 In zero-sum games, the concept of the Nash Equilibrium is often used to analyze and predict the outcome of the game. The Nash Equilibrium is a state in which each player's strategy is optimal given the strategies of the other players, and no player has the incentive to change their strategy. In a zero-sum game, the Nash Equilibrium represents the most balanced outcome, with one player's gain being exactly offset by the losses of the other players. In zero-sum games, the concept of the Nash Equilibrium is often used to analyze and predict the outcome of the game. The Nash Equilibrium is a state in which each player's strategy is optimal given the strategies of the other players, and no player has the incentive to change their strategy. In a zero-sum game, the Nash Equilibrium represents the most balanced outcome, with one player's gain being exactly offset by the losses of the other players.
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 =====Positive-Sum Game Theory===== =====Positive-Sum Game Theory=====
  
-A positive-sum game is one in which the total benefit or gain of all players in the game is greater than zero. In other words, in a positive-sum game, the collective benefit of all players is increased as a result of their interaction.+A positive-sum game[(win_game>Win–win game[[https://en.wikipedia.org/wiki/Win%E2%80%93win_game|Wikipedia]])] 
 + is one in which the total benefit or gain of all players in the game is greater than zero. In other words, in a positive-sum game, the collective benefit of all players is increased as a result of their interaction.
  
 Positive-sum games are often characterized by cooperation and mutual benefit, where the actions of one player can lead to increased benefits for all players. For example, trade between countries can be seen as a positive-sum game, where both countries benefit from the exchange of goods and services. Another example is a cooperative game, where players work together to achieve a common goal, and each player's efforts increase the overall benefit for all players. Positive-sum games are often characterized by cooperation and mutual benefit, where the actions of one player can lead to increased benefits for all players. For example, trade between countries can be seen as a positive-sum game, where both countries benefit from the exchange of goods and services. Another example is a cooperative game, where players work together to achieve a common goal, and each player's efforts increase the overall benefit for all players.
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 Negative-sum games present challenges in terms of finding solutions that lead to a more positive outcome for all players involved. They often require cooperation, compromise, and a willingness to sacrifice individual benefits for the collective good. Negative-sum games present challenges in terms of finding solutions that lead to a more positive outcome for all players involved. They often require cooperation, compromise, and a willingness to sacrifice individual benefits for the collective good.
  
-} 
 =====The Prisoner's Dilemma===== =====The Prisoner's Dilemma=====
  
-The prisoner's dilemma is a classic example of a non-cooperative game in game theory, used to illustrate the conflicts that can arise from rational self-interest. It is a two-player game that models a situation in which two individuals are accused of a crime and are held in separate cells, unable to communicate with each other. {{ :prisoners_dilemma.png?nolink&400|}}+The prisoner's dilemma[(Prisoners_dilemma>Prisoner's dilemma[[https://en.wikipedia.org/wiki/Prisoner%27s_dilemma|Wikipedia]])] 
 + is a classic example of a non-cooperative game in game theory, used to illustrate the conflicts that can arise from rational self-interest. It is a two-player game that models a situation in which two individuals are accused of a crime and are held in separate cells, unable to communicate with each other. {{ :prisoners_dilemma.png?nolink&400|}}
  
 In the game, each player must decide whether to confess or remain silent. If both players confess, they both receive a severe punishment. If both players remain silent, they receive a lesser punishment. If one player confesses and the other remains silent, the player who confesses receives a reduced punishment while the other player receives a severe punishment. In the game, each player must decide whether to confess or remain silent. If both players confess, they both receive a severe punishment. If both players remain silent, they receive a lesser punishment. If one player confesses and the other remains silent, the player who confesses receives a reduced punishment while the other player receives a severe punishment.
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 The prisoner's dilemma provides a powerful illustration of the challenges and conflicts that can arise from rational self-interest and the importance of cooperation in achieving mutually beneficial outcomes. The prisoner's dilemma provides a powerful illustration of the challenges and conflicts that can arise from rational self-interest and the importance of cooperation in achieving mutually beneficial outcomes.
  
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 =====Other Common Examples of Game Theory===== =====Other Common Examples of Game Theory=====
  
 There are many other examples of game theory, some of which are: There are many other examples of game theory, some of which are:
  
-  * **Chicken**: This is a game in which two drivers race towards each other on a collision course. The driver who swerves first is the loser, while the driver who continues straight on is the winner.+  * **Chicken**[(chucken>Chicken (game)[[https://en.wikipedia.org/wiki/Chicken_(game)|Wikipedia]])]: This is a game in which two drivers race towards each other on a collision course. The driver who swerves first is the loser, while the driver who continues straight on is the winner.
  
-  * **Tragedy of the Commons**: This is a game in which multiple individuals share a common resource, such as a fishery or a forest, and must decide how much of the resource to extract. If all individuals extract as much as they can, the resource becomes depleted and everyone is worse off.+  * **Tragedy of the Commons**[(Tragedy_of_the_commons>Tragedy of the commons[[https://en.wikipedia.org/wiki/Tragedy_of_the_commons|Wikipedia]])]: This is a game in which multiple individuals share a common resource, such as a fishery or a forest, and must decide how much of the resource to extract. If all individuals extract as much as they can, the resource becomes depleted and everyone is worse off.
  
-  * **Stag Hunt**: This is a game in which two individuals must decide whether to hunt a stag or a hare. Hunting a stag requires cooperation, while hunting a hare can be done individually. If one person hunts a stag and the other hunts a hare, the person who hunted the stag will be left empty-handed.+  * **Stag Hunt**[(Staghunt>Stag hunt[[https://en.wikipedia.org/wiki/Stag_hunt|Wikipedia]])]: This is a game in which two individuals must decide whether to hunt a stag or a hare. Hunting a stag requires cooperation, while hunting a hare can be done individually. If one person hunts a stag and the other hunts a hare, the person who hunted the stag will be left empty-handed.
  
-  * **Battle of the Sexes**: This is a game in which a couple must decide whether to attend a ballet or a football game. If they both attend the same event, they are both happy. If they attend different events, they will both be unhappy.+  * **Battle of the Sexes**[(Battle_of_the_sexes_>Battle of the sexes (game theory)[[https://en.wikipedia.org/wiki/Battle_of_the_sexes_(game_theory)|Wikipedia]])]: This is a game in which a couple must decide whether to attend a ballet or a football game. If they both attend the same event, they are both happy. If they attend different events, they will both be unhappy.
  
-  * **Ultimatum Game**: This is a game in which one player must make a proposal for how to divide a sum of money between the two players. The other player must then decide whether to accept or reject the proposal. If the proposal is rejected, both players receive nothing.+  * **Ultimatum Game**[(Ultimatum>Ultimatum game[[https://en.wikipedia.org/wiki/Ultimatum_game|Wikipedia]])]: This is a game in which one player must make a proposal for how to divide a sum of money between the two players. The other player must then decide whether to accept or reject the proposal. If the proposal is rejected, both players receive nothing.
  
 These games illustrate different aspects of game theory and decision-making and are used to study various aspects of human behavior, including cooperation, competition, fairness, and bargaining. These games illustrate different aspects of game theory and decision-making and are used to study various aspects of human behavior, including cooperation, competition, fairness, and bargaining.
 +
 +A Game Theory course from Stanford University is available for free by Stanford Online [[https://online.stanford.edu/courses/soe-ycs0002-game-theory| Game Theory by Matthew O. Jackson, Kevin Leyton-Brown, Yoav Shoham]].
  
 =====Tragedy of The Commons===== =====Tragedy of The Commons=====
  
-The Tragedy of the Commons is a concept in game theory that describes a situation in which multiple individuals share a common resource, such as a fishery or a forest, and must decide how much of the resource to extract. In this game, each individual acts in their own self-interest and tries to maximize their extraction of the resource. However, if all individuals extract as much as they can, the resource becomes depleted and everyone is worse off.+The Tragedy of the Commons[(Tragedy_of_the_commons)] is a concept in game theory that describes a situation in which multiple individuals share a common resource, such as a fishery or a forest, and must decide how much of the resource to extract. In this game, each individual acts in their own self-interest and tries to maximize their extraction of the resource. However, if all individuals extract as much as they can, the resource becomes depleted and everyone is worse off. 
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 The Tragedy of the Commons is often referred to as a "tragedy" because the outcome is not in the best interest of the group as a whole, despite each individual acting in their own self-interest. The tragedy occurs because there is a lack of incentives for individuals to conserve the resource and a lack of mechanisms for enforcing conservation. The Tragedy of the Commons is often referred to as a "tragedy" because the outcome is not in the best interest of the group as a whole, despite each individual acting in their own self-interest. The tragedy occurs because there is a lack of incentives for individuals to conserve the resource and a lack of mechanisms for enforcing conservation.
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 ====Tragedy of The Commons and Narcisissm==== ====Tragedy of The Commons and Narcisissm====
  
-The relationship between narcissism and the Tragedy of the Commons game theory can be seen in the sense that individuals with narcissistic tendencies may prioritise their own needs and desires and act in their own self-interest at the expense of the group or relationship as a whole. This behaviour can be seen as a form of "emotional depletion" of the group or relationship, similar to the depletion of a common resource in the Tragedy of the Commons game.+The relationship between narcissism and the Tragedy of the Commons game theory[(0146167205274855>Understanding the social costs of narcissism: the case of the tragedy of the commons[[https://pubmed.ncbi.nlm.nih.gov/16143668/|Pers Soc Psychol Bull. 2005 Oct;31(10):1358-68.doi: 10.1177/0146167205274855.]])] 
 + can be seen in the sense that individuals with narcissistic tendencies may prioritise their own needs and desires and act in their own self-interest at the expense of the group or relationship as a whole. This behaviour can be seen as a form of "emotional depletion" of the group or relationship, similar to the depletion of a common resource in the Tragedy of the Commons game.
  
 In situations where a narcissistic individual is part of a group or relationship, their actions and decisions may prioritise their own desires and needs, leading to a breakdown in communication, cooperation, and trust within the group or relationship. This can result in a decrease in the emotional well-being and satisfaction of the group or relationship as a whole, similar to the tragedy that occurs in the Tragedy of the Commons game. In situations where a narcissistic individual is part of a group or relationship, their actions and decisions may prioritise their own desires and needs, leading to a breakdown in communication, cooperation, and trust within the group or relationship. This can result in a decrease in the emotional well-being and satisfaction of the group or relationship as a whole, similar to the tragedy that occurs in the Tragedy of the Commons game.
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  • Last modified: 2023/02/08 22:59
  • by roni