On the level of cooperative behavior in a local-interaction model

Abstract

We study local interaction within a population located on a connected graph. Subjects engage in several bilateral interactions during each round in a generalized Prisoners' Dilemma (PD). In each round of play one randomly selected player gets the possibility to update the action he plays in this PD. All individuals use the update rule “Win Cooperate, Lose Defect,” a multi-player variant of Tit-for-Tat. Theoretical results on the set of stable states of the associated dynamics are provided for the cases with and without rare mutations. Simulations provide insight into the probability distribution over these stable states. In both cases a rather high probability is assigned to stable states with a moderate level of cooperation implying that dominated strategies are used. Furthermore, the probability of reaching the stable state with Nash equilibrium play is small.