确定性离散时间演化博弈动力学中的周期轨道：信息论视角
Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective
AI总结：
针对演化博弈中非收敛周期轨道缺乏博弈论解释的问题，引入相对熵提出演化稳定策略的推广概念“信息稳定轨道”，并探讨其与动力学稳定性的联系。
摘要：
尽管在生态和演化背景下种群状态的非收敛演化存在性是一个不可否认的事实，但在演化博弈论文献中，对此类结果具有深刻见解的博弈论解释却寥寥无几。作为概念验证，我们引入信息论中的相对熵概念，旨在为一大类确定性离散时间演化博弈动力学中的周期轨道构建博弈论解释，主要研究双人双策略情形。实际上，我们提出了演化稳定策略（演化博弈理论的基石）的一致性推广，并将其恰当地命名为：信息稳定轨道。信息稳定轨道捕捉了演化稳定策略的本质，即它将演化突变体所获得的总收益与突变体与自身博弈时所获得的总收益进行比较。此外，我们还讨论了信息稳定轨道与相应周期轨道动力学稳定性之间的联系。
英文摘要：
Even though existence of non-convergent evolution of the states of populations in ecological and evolutionary contexts is an undeniable fact, insightful game-theoretic interpretations of such outcomes are scarce in the literature of evolutionary game theory. As a proof-of-concept, we tap into the information-theoretic concept of relative entropy in order to construct a game-theoretic interpretation for periodic orbits in a wide class of deterministic discrete-time evolutionary game dynamics, primarily investigating the two-player two-strategy case. Effectively, we present a consistent generalization of the evolutionarily stable strategy -- the cornerstone of the evolutionary game theory -- and aptly term the generalized concept: information stable orbit. The information stable orbit captures the essence of the evolutionarily stable strategy in that it compares the total payoff obtained against an evolving mutant with the total payoff that the mutant gets while playing against itself. Furthermore, we discuss the connection of the information stable orbit with the dynamical stability of the corresponding periodic orbit.
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