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17-04-2021 | Issue 4/2021

Dynamic Games and Applications 4/2021

Effect of Variability in Payoffs on Conditions for the Evolution of Cooperation in a Small Population

Journal:
Dynamic Games and Applications > Issue 4/2021
Authors:
Dhaker Kroumi, Éloi Martin, Cong Li, Sabin Lessard
Important notes
Research is supported in part by the Deanship of Scientific Research (DSR) at King Fahd University of Petroleum and Minerals (KFUPM) and the Natural Sciences and Engineering Research Council of Canada.

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Abstract

In this paper, we study the effect of stochastic fluctuations in payoffs for two strategies, cooperation and defection, used in random pairwise interactions in a population of fixed finite size with an update according to a Moran model. We assume that the means, variances and covariances of the payoffs are of the same small order while all higher-order moments are negligible. We show that more variability in the payoffs to defection and less variability in the payoffs to cooperation contribute to the evolutionary success of cooperation over defection as measured by fixation probabilities under weak selection. This conclusion is drawn by comparing the probabilities of ultimate fixation of cooperation and defection as single mutants to each other and to what they would be under neutrality. These comparisons are examined in detail with respect to the population size and the second moments of the payoffs in five cases of additive Prisoner’s Dilemmas. The analysis is extended to a Prisoner’s Dilemma repeated a random number of times with Tit-for-Tat starting with cooperation and Always-Defect as strategies. Moreover, simulations with an update according to a Wright–Fisher model suggest that the conclusions are robust.

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