Asymptotic behavior of strategies in the repeated prisoner’s dilemma game in the presence of errors

Abstract

We examine the asymptotic behavior of a finite, but error-prone population, whose agents can choose one of ALLD (alwaysdefect), ALLC (always cooperate), or Pavlov (repeats the previous action if the opponent cooperated and changes action otherwise)to play the repeated Prisoner’s Dilemma. A novelty of the study is that it allows for three types of errors that affect agents’strategies in distinct ways: (a) implementation errors, (b) perception errors of one’s own action, and (c) perception errors of theopponent’s action. We also derive numerical results based on the payoff matrix used in the tournaments of Axelrod. Strategies’payoffs are monitored as the likelihood of committing errors increases from zero to one, which enables us to provide a taxonomyof best response strategies. We find that for some range of error levels, a unique best response (i.e. a dominant strategy) exists. Inall other, the population composition can vary based on the proportion of each strategist’s type and/or the payoffs of the matrix.Overall, our results indicate that the emergence of cooperation is considerably weak at most error levels.