Stochastically Stable Equilibria for Evolutionary Snowdrift Games on Graphs

In this paper, we study two-player evolutionary snowdrift games 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 games on graphs. If the benefit-to-cost ratio is greater than 1.5, then the proportion of cooperators of a regular graph is higher than that of well-mixed population. And for BD and PC updating, the smaller graph degree can lead to more cooperators. Besides theoretical analysis, the results are also demonstrated by numerical simulations.