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.

翻译：尽管生态和进化背景下种群状态的非收敛演化是一个不可否认的事实，但在演化博弈理论的文献中，对此类结果富有洞见的博弈论解释却十分罕见。作为概念验证，我们利用信息论中的相对熵概念，为一类广泛的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，主要研究两人两策略情形。实际上，我们对演化稳定策略——演化博弈理论的基石——提出了一致的推广，并恰当地将这一推广概念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，即比较针对演化突变体所获得的总收益与该突变体在对抗自身时所获得的总收益。此外，我们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。