Regular Article - Statistical and Nonlinear Physics
Statistics of the number of equilibria in random social dilemma evolutionary games with mutation
School of Mathematics, University of Birmingham, B15 2TT, Birmingham, UK
2 School of Computing, Engineering and Digital Technologies, Teesside University, TS1 3BX, Middlesbrough, UK
Accepted: 9 August 2021
Published online: 23 August 2021
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.
© The Author(s) 2021
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