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Evolutionary game dynamics in a Wright-Fisher process

机译：Wright-Fisher过程中的进化游戏动力学

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Evolutionary game dynamics in finite populations can be described by a frequency dependent, stochastic Wright-Fisher process. We consider a symmetric game between two strategies, A and B. There are discrete generations. In each generation, individuals produce offspring proportional to their payoff. The next generation is sampled randomly from this pool of offspring. The total population size is constant. The resulting Markov process has two absorbing states corresponding to homogeneous populations of all A or all B. We quantify frequency dependent selection by comparing the absorption probabilities to the corresponding probabilities under random drift. We derive conditions for selection to favor one strategy or the other by using the concept of total positivity. In the limit of weak selection, we obtain the 1/3 law: if A and B are strict Nash equilibria then selection favors replacement of B by A, if the unstable equilibrium occurs at a frequency of A which is less than 1/3.
机译：有限种群中的演化博弈动力学可以通过频率相关的随机Wright-Fisher过程来描述。我们考虑两种策略A和B之间的对称博弈。存在离散的代。在每一代中，个体都会产生与其收益成正比的后代。从该后代库中随机抽取下一代。总人口规模是恒定的。所得的马尔可夫过程具有对应于所有A或所有B的均质种群的两个吸收状态。我们通过比较吸收概率与随机漂移下的相应概率来量化频率依赖性选择。通过使用总积极性的概念，我们得出选择条件以偏向一种策略或另一种策略。在弱选择的极限中，我们获得了1/3定律：如果A和B是严格的纳什均衡，那么如果不稳定的平衡出现在A的频率小于1/3时，选择则倾向于用A替代B。

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