Stochastic Stability of Evolutionary Prisoner’s Dilemma*

Abstract

In this paper, we study two-player evolutionary prisoner’s dilemma on regular graphs and identify the stochastically stable equilibria for infinite populations. We consider four different update rules: birth-death(BD), death-birth(DB), imitation(IM) and pairwise comparison(PC). With the same values of cost and benefit of cooperation, we show that there is a unique stochastically stable equilibrium for evolutionary prisoner’s dilemma on regular graphs. If the benefit-to-cost ratio is larger than k + 2 (k is the degree of a regular graph), the networked game has a higher fraction of cooperators than that for a well-mixed population. Under certain conditions, the lower graph connectivity can lead to the emergence of more cooperators. Besides theoretical analysis, we demonstrate our results through numerical computations and simulations as well.