Analysis and shifting of stochastically stable equilibria for evolutionary snowdrift games

In this paper we investigate the stochastic stability of evolutionary snowdrift games, which belong to a class of standard games popular in theoretical biology for the study of the mechanism of the emergence and maintenance of cooperation in large populations of strategically interacting individuals. We identify stochastically stable equilibria for two-player and multi-player evolutionary snowdrift games, for which the existing results are almost exclusively on the former. For the two cases with the same values of cost and benefit of cooperation, we show that like the two-player case, under certain conditions, there is a unique stochastically stable equilibrium in the multi-player case, at which, however, the proportion of cooperators can be higher than that of the two-player case. More importantly, the proportion of cooperators can be manipulated as the stochastically stable equilibrium is being shifted by changing the game parameters. So the results indicate a promising approach to controlling the proportion of cooperators in large populations that has not been reported before. Besides theoretical analysis, we demonstrate our results through numerical computations and simulations as well.