Instability of Defection in the Prisoner’s Dilemma: Best Experienced Payoff Dynamics Analysis

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.

Sampling Dynamics and Stable Mixing in Hawk-Dove Games

“…The payoff-sampling dynamics were pioneered by Osborne and Rubinstein (1998) and Sethi (2000) and later generalized in various respects by Sandholm et al (2020). It has been used in a variety of applications, including price competition with boundedly rational consumers (Spiegler, 2006), common-pool resources (Cárdenas et al, 2015), contributions to public goods (Mantilla et al, 2018), centipede games (Sandholm et al, 2019), finitely repeated games (Sethi, 2019) and the prisoner's dilemma (Arigapudi et al, 2021). The existing literature assumes that all agents have the same sample size.…”