{"title":"Introspection Dynamics in Asymmetric Multiplayer Games","authors":"Marta C. Couto, Saptarshi Pal","doi":"10.1007/s13235-023-00525-8","DOIUrl":null,"url":null,"abstract":"Abstract Evolutionary game theory and models of learning provide powerful frameworks to describe strategic decision-making in social interactions. In the simplest case, these models describe games among two identical players. However, many interactions in everyday life are more complex. They involve more than two players who may differ in their available actions and in their incentives to choose each action. Such interactions can be captured by asymmetric multiplayer games. Recently, introspection dynamics has been introduced to explore such asymmetric games. According to this dynamics, at each time step players compare their current strategy to an alternative strategy. If the alternative strategy results in a payoff advantage, it is more likely adopted. This model provides a simple way to compute the players’ long-run probability of adopting each of their strategies. In this paper, we extend some of the previous results of introspection dynamics for 2-player asymmetric games to games with arbitrarily many players. First, we derive a formula that allows us to numerically compute the stationary distribution of introspection dynamics for any multiplayer asymmetric game. Second, we obtain explicit expressions of the stationary distribution for two special cases. These cases are additive games (where the payoff difference that a player gains by unilaterally switching to a different action is independent of the actions of their co-players), and symmetric multiplayer games with two strategies. To illustrate our results, we revisit several classical games such as the public goods game.","PeriodicalId":48933,"journal":{"name":"Dynamic Games and Applications","volume":"239 1","pages":"0"},"PeriodicalIF":1.8000,"publicationDate":"2023-09-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Dynamic Games and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s13235-023-00525-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 1
Abstract
Abstract Evolutionary game theory and models of learning provide powerful frameworks to describe strategic decision-making in social interactions. In the simplest case, these models describe games among two identical players. However, many interactions in everyday life are more complex. They involve more than two players who may differ in their available actions and in their incentives to choose each action. Such interactions can be captured by asymmetric multiplayer games. Recently, introspection dynamics has been introduced to explore such asymmetric games. According to this dynamics, at each time step players compare their current strategy to an alternative strategy. If the alternative strategy results in a payoff advantage, it is more likely adopted. This model provides a simple way to compute the players’ long-run probability of adopting each of their strategies. In this paper, we extend some of the previous results of introspection dynamics for 2-player asymmetric games to games with arbitrarily many players. First, we derive a formula that allows us to numerically compute the stationary distribution of introspection dynamics for any multiplayer asymmetric game. Second, we obtain explicit expressions of the stationary distribution for two special cases. These cases are additive games (where the payoff difference that a player gains by unilaterally switching to a different action is independent of the actions of their co-players), and symmetric multiplayer games with two strategies. To illustrate our results, we revisit several classical games such as the public goods game.
期刊介绍:
Dynamic Games and Applications is devoted to the development of all classes of dynamic games, namely, differential games, discrete-time dynamic games, evolutionary games, repeated and stochastic games, and their applications in all fields