Classical studies in evolutionary game theory assume constant payoffs. Randomly fluctuating environments in real populations make this assumption idealistic. In this paper, we study randomized two-player linear games in a finite population in a succession of birth-death events according to a Moran process and in the presence of symmetric mutation. Introducing identity measures under neutrality that depend on the mutation rate and calculating these in the limit of a large population size by using the coalescent process, we study the first-order effect of the means, variances and covariances of the payoffs on average abundance in the stationary state under mutation and selection. This shows how the average abundance of a strategy is driven not only by its mean payoffs but also by the variances and covariances of its payoffs. In Prisoner’s Dilemmas with additive cost and benefit for cooperation, where constant payoffs always favor the abundance of defection, stochastic fluctuations in the payoffs can change the strategy that is more abundant on average in the stationary state. The average abundance of cooperation is increased if the variance of any payoff to cooperation against cooperation or defection, or their covariance, is decreased, or if the variance of any payoff to defection against cooperation or defection, or their covariance, is increased. This is also the case for a Prisoner’s Dilemma with independent payoffs that is repeated a random number of times. As for the mutation rate, it comes into play in the coefficients of the variances and covariances that determine average abundance. Increasing the mutation rate can enhance or lessen the condition for a strategy to be more abundant on average than another.

进化博弈论中的经典研究假设收益是恒定的。实际人口中随机波动的环境使这一假设变得理想化。在本文中，我们根据Moran过程并在对称突变的情况下，在一系列出生死亡事件中研究有限种群中的随机两人线性游戏。引入依赖于突变率的中性条件下的同一性度量，并通过合并过程在较大的人口规模范围内对其进行计算，我们研究收益的均值，方差和协方差对平均丰度的一阶效应。突变和选择下的稳态。这表明策略的平均丰度不仅由其平均收益驱动，还由其收益的方差和协方差驱动。在具有附加成本和合作收益的“囚徒困境”中，持续的收益总是偏爱大量的叛逃，收益的随机波动会改变策略，这种策略在固定状态下平均更为丰富。如果减少了针对合作或叛逃的合作收益或它们的协方差的方差，或者如果针对合作或叛逃的叛变所获得的收益的方差或它们的协方差增加了，那么平均合作丰度就会增加。对于具有独立收益的囚徒困境，情况也是如此，重复随机次数。至于突变率，它决定了平均丰度的方差和协方差系数。