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Instability of defection in the prisoner’s dilemma under best experienced payoff dynamics

Arigapudi, Srinivas and Heller, Yuval and Milchtaich, Igal (2021): Instability of defection in the prisoner’s dilemma under best experienced payoff dynamics. Forthcoming in: Journal of Economic Theory

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Abstract

We study population dynamics under which each revising agent tests each strategy k times, with each trial being against a newly drawn opponent, and chooses the strategy whose mean payoff was highest. When k = 1, defection is globally stable in the prisoner’s dilemma. By contrast, when k > 1 we show that there exists a globally stable state in which agents cooperate with probability between 28% and 50%. Next, we characterize stability of strict equilibria in general games. Our results demonstrate that the empirically-plausible case of k > 1 can yield qualitatively different predictions than the case of k = 1 that is commonly studied in the literature.

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