博弈的竞争演化动力学
Purely competitive evolutionary dynamics for games
摘要：
我们介绍和分析了一个纯粹的竞争动力学的无限人口的3-策略游戏的发展。我们认为，这种动力学代表了某些系统，无论是自然的和人工的，是如何治理的表征。在每个阶段，种群被随机分成两对，参与一次性游戏;成员将其类型传播给后代的概率仅与其在配对中的收益成比例。我们表明，如果一种类型是占主导地位的（获得更高的收益与其他两种类型的游戏），其“纯”的人口状态，只包括该类型的成员，是全球吸引。如果没有主导类型，则存在不稳定的“混合”不动点;布居态最终在三个近纯态之间振荡。然后我们允许突变，其中后代具有随机改变其类型的非零概率。在这种情况下，一个主导类型的存在使一个点在其纯态附近全局吸引。如果不存在显性类型，则在唯一的混合不动点处发生超临界Hopf分岔，并且在临界（通常较低）突变率以上，该不动点变得全局吸引：这意味着即使非常低的突变率也可以稳定在没有突变的情况下不稳定的系统。
英文摘要：
We introduce and analyze a purely competitive dynamics for the evolution of an infinite population subject to a 3-strategy game. We argue that this dynamics represents a characterization of how certain systems, both natural and artificial, are governed. In each period, the population is randomly sorted into pairs, which engage in a once-off play of the game; the probability that a member propagates its type to its offspring is proportional only to its payoff within the pair. We show that if a type is dominant (obtains higher payoffs in games with both other types), its 'pure' population state, comprising only members of that type, is globally attracting. If there is no dominant type, there is an unstable 'mixed' fixed point; the population state eventually oscillates between the three near-pure states. We then allow for mutations, where offspring have a non-zero probability of randomly changing their type. In this case, the existence of a dominant type renders a point near its pure state globally attracting. If no dominant type exists, a supercritical Hopf bifurcation occurs at the unique mixed fixed point, and above a critical (typically low) mutation rate, this fixed point becomes globally attracting: the implication is that even very low mutation rates can stabilize a system that would, in the absence of mutations, be unstable.
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