论文标题
确定性离散时间进化游戏动力学中的周期性轨道：信息理论观点
Periodic orbits in deterministic discrete-time evolutionary game dynamics: An information-theoretic perspective
论文作者
论文摘要
尽管在生态和进化环境中人口状态的非赋值发展是一个不可否认的事实，但在进化游戏理论的文献中，对这种结果的有见地的游戏理论解释是稀缺的。作为概念验证，我们利用了相对熵的信息理论概念，以便在广泛的确定性离散时间进化游戏动力学中为周期性轨道构建游戏理论解释，主要研究了两者的两策略案例。有效地，我们提出了对进化稳定策略的一致概括（进化游戏理论的基石），并恰当地称为广义概念：信息稳定的轨道。信息稳定的轨道捕获了进化稳定策略的本质，因为它比较了与不断发展的突变体获得的总收益与突变体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的动态稳定性的联系。
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.
