带突变的石头剪刀布博弈的非线性动力学
Nonlinear Dynamics of the Rock-Paper-Scissors Game with Mutations
摘要：
我们分析了石头剪刀布游戏的复制-变异方程。各种图论模式的突变被认为是，从一个单一的单向突变途径之间的两个物种，全球所有物种之间的双向突变。我们的主要结果是，共存状态，其中所有三个物种存在于平衡，可以通过任意小的突变率不稳定。当共存态失去稳定性后，在超临界Hopf分岔中产生一个稳定极限环解。该吸引周期解对所有的突变模式都存在，并且在零突变率和零和对策的极限附近任意持续存在。
英文摘要：
We analyze the replicator-mutator equations for the Rock-Paper-Scissors game. Various graph-theoretic patterns of mutation are considered, ranging from a single unidirectional mutation pathway between two of the species, to global bidirectional mutation among all the species. Our main result is that the coexistence state, in which all three species exist in equilibrium, can be destabilized by arbitrarily small mutation rates. After it loses stability, the coexistence state gives birth to a stable limit cycle solution created in a supercritical Hopf bifurcation. This attracting periodic solution exists for all the mutation patterns considered, and persists arbitrarily close to the limit of zero mutation rate and a zero-sum game.
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