Using chemical reaction network theory to show stability of distributional dynamics in game theory

IF 1.1 Q3 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
R. Cressman, V. Křivan
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引用次数: 0

Abstract

This article shows how to apply results of chemical reaction network theory (CRNT) to prove uniqueness and stability of a positive equilibrium for pairs/groups distributional dynamics that arise in game theoretic models. Evolutionary game theory assumes that individuals accrue their fitness through interactions with other individuals. When there are two or more different strategies in the population, this theory assumes that pairs (groups) are formed instantaneously and randomly so that the corresponding pairs (groups) distribution is described by the Hardy–Weinberg (binomial) distribution. If interactions times are phenotype dependent the Hardy-Weinberg distribution does not apply. Even if it becomes impossible to calculate the pairs/groups distribution analytically we show that CRNT is a general tool that is very useful to prove not only existence of the equilibrium, but also its stability. In this article, we apply CRNT to pair formation model that arises in two player games (e.g., Hawk-Dove, Prisoner's Dilemma game), to group formation that arises, e.g., in Public Goods Game, and to distribution of a single population in patchy environments. We also show by generalizing the Battle of the Sexes game that the methodology does not always apply.
用化学反应网络理论说明博弈论中分布动力学的稳定性
本文展示了如何应用化学反应网络理论(CRNT)的结果来证明博弈论模型中出现的对/群分布动力学的正平衡的唯一性和稳定性。进化博弈论认为,个体通过与其他个体的相互作用而获得适合度。当总体中存在两种或两种以上不同的策略时,该理论假定成对(组)是瞬间随机形成的,因此相应的成对(组)分布用Hardy-Weinberg(二项)分布来描述。如果相互作用时间依赖于表型,那么Hardy-Weinberg分布就不适用。即使无法解析计算对/群分布,我们也证明了CRNT是一个通用的工具,它不仅可以证明平衡的存在性,而且可以证明平衡的稳定性。在本文中,我们将CRNT应用于两人博弈(如鹰鸽博弈、囚徒困境博弈)中出现的配对形成模型、公共物品博弈中出现的群体形成模型以及斑块环境中单个人口的分布。我们还通过推广“性别之战”游戏来证明,这种方法并不总是适用。
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来源期刊
Journal of Dynamics and Games
Journal of Dynamics and Games MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-
CiteScore
2.00
自引率
0.00%
发文量
26
期刊介绍: The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.
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