The European Physical Journal B ( IF 1.6 ) Pub Date : 2021-08-23 , DOI: 10.1140/epjb/s10051-021-00181-0 Manh Hong Duong 1 , The Anh Han 2
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Abstract
In this paper, we study analytically the statistics of the number of equilibria in pairwise social dilemma evolutionary games with mutation where a game’s payoff entries are random variables. Using the replicator–mutator equations, we provide explicit formulas for the probability distributions of the number of equilibria as well as other statistical quantities. This analysis is highly relevant assuming that one might know the nature of a social dilemma game at hand (e.g., cooperation vs coordination vs anti-coordination), but measuring the exact values of its payoff entries is difficult. Our delicate analysis shows clearly the influence of the mutation probability on these probability distributions, providing insights into how varying this important factor impacts the overall behavioural or biological diversity of the underlying evolutionary systems.
Graphic abstract
中文翻译：
具有变异的随机社会困境进化博弈中均衡数的统计
摘要
在本文中，我们分析研究了具有突变的成对社会困境进化博弈中均衡数的统计，其中博弈的收益条目是随机变量。使用复制器-增变器方程，我们为均衡数的概率分布以及其他统计量提供了明确的公式。假设人们可能知道手头的社交困境博弈的性质（例如，合作 vs 协调 vs 反协调），这种分析是高度相关的，但很难衡量其收益条目的确切值。我们细致的分析清楚地显示了突变概率对这些概率分布的影响，
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