论文标题
多玩家游戏的平均合作丰富性，并随机回报
Average abundancy of cooperation in multi-player games with random payoffs
论文作者
论文摘要
我们考虑在尺寸$ d \ geq2 $组中的玩家与收益之间的互动，这些收益不仅取决于小组中使用的策略，而且随着时间的推移随着时间的流逝而随机波动。一个人可以通过莫兰模型通过出生死亡事件将合作或叛逃作为策略作为策略，从一次性步骤更新到下一步。假设具有相同小阶的预期值，方差和协方差的反复对称突变和回报，我们将在选择符合的平衡中得出平均合作的一阶近似。我们表明，增加叛逃的任何回报的差异或减少合作回报的差异会增加合作的平均丰度。至于任何合作回报与任何叛逃的回报之间的协方差的影响，我们表明这取决于与这些回报相关的组中合作者的数量。我们特别研究了公共物品游戏，雄鹿狩猎游戏和雪花游戏，所有社交困境都基于随机收益$ b $和合作的费用$ c $。我们表明，$ b $或$ c $的规模差异的减少，或增加其缩放协方差，使弱选择更容易偏爱雄鹿狩猎游戏和雪花游戏中的丰富合作。公共物品游戏的结论相同，只是$ b $的协方差对$ c $的平均丰度没有影响。另一方面，提高缩放的突变率或组大小可以增强或减少弱选择的条件，从而有利于$ c $的丰度。
We consider interactions between players in groups of size $d\geq2$ with payoffs that not only depend on the strategies used in the group but also fluctuate at random over time. An individual can adopt either cooperation or defection as strategy and the population is updated from one-time step to the next by a birth-death event according to a Moran model. Assuming recurrent symmetric mutation and payoffs with expected values, variances, and covariances of the same small order, we derive a first-order approximation of the average abundance of cooperation in the selection-mutation equilibrium. We show that increasing the variance of any payoff for defection or decreasing the variance of any payoff for cooperation increases the average abundance of cooperation. As for the effect of the covariance between any payoff for cooperation and any payoff for defection, we show that it depends on the number of cooperators in the group associated with these payoffs. We study in particular the public goods game, the stag hunt game, and the snowdrift game, all social dilemmas based on random benefit $b$ and cost $c$ for cooperation. We show that a decrease in the scaled variance of $b$ or $c$, or an increase in their scaled covariance, makes it easier for weak selection to favor the abundance of cooperation in the stag hunt game and the snowdrift game. The same conclusion holds for the public goods game except that the covariance of $b$ has no effect on the average abundance of $C$. On the other hand, increasing the scaled mutation rate or the group size can enhance or lessen the condition for weak selection to favor the abundance of $C$.
