Instability of Defection in the Prisoner’s Dilemma Under Best Experienced Payoff Dynamics
Srinivas Arigapudi, Yuval Heller and Igal Milchtaich
Journal of Economic Theory 197 (2021), 105174
We study population dynamics under which each revising agent tests each action k times, with each trial being against a newly drawn opponent, and chooses the action whose mean payoff was highest during the testing phase. When k = 1, defection is globally stable in the prisoner's dilemma. By contrast, when k > 1 we show that, if the gains from defection are not too large, 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 k = 1 commonly studied in the literature.
Learning; Cooperation; Best experienced payoff dynamics; Sampling equilibrium; Evolutionary stability.