非对称多人游戏中的内省动态

IF 16.4 1区 化学 Q1 CHEMISTRY, MULTIDISCIPLINARY
Marta C. Couto, Saptarshi Pal
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引用次数: 1

摘要

进化博弈论和学习模型为描述社会互动中的战略决策提供了强有力的框架。在最简单的情况下,这些模型描述的是两个相同玩家之间的博弈。然而,日常生活中的许多互动要复杂得多。这类游戏涉及两个以上的玩家,他们的可用行动和选择每个行动的动机可能不同。非对称多人游戏可以捕捉到这种互动。最近,内省动力学被引入来探索这种不对称博弈。根据这一动态,玩家在每个时间步都会将当前策略与备选策略进行比较。如果备选策略产生收益优势,则更有可能被采用。这个模型提供了一种简单的方法来计算参与者采用各自策略的长期概率。在本文中,我们将之前关于2人非对称博弈的内省动力学的一些结果扩展到具有任意多玩家的博弈。首先,我们推导出一个公式,使我们能够数值计算任何多人非对称游戏的内省动态的平稳分布。其次,我们得到了两种特殊情况下平稳分布的显式表达式。这些例子是附加游戏(游戏邦注:即玩家单方面转向不同行动所获得的收益差异与其他玩家的行动无关),以及带有两种策略的对称多人游戏。为了说明我们的结果,我们回顾了几个经典游戏,如公共物品游戏。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Introspection Dynamics in Asymmetric Multiplayer Games
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.
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来源期刊
Accounts of Chemical Research
Accounts of Chemical Research 化学-化学综合
CiteScore
31.40
自引率
1.10%
发文量
312
审稿时长
2 months
期刊介绍: Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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