Complex interactions promote the frequency of cooperation in snowdrift game

The emergence and maintains of cooperation in social dilemmas is one of the most popular problem in evolutionary game theory. In this paper, we consider the influence of complex interactions in evolutionary game theory. We consider a situation that some individuals may get additional benefits in snowdrift game without the detriment of the co-player because of difference in status, like good reputation of assisting the weak. We find that the replicator dynamics of asymmetric snowdrift game have one boundary stable equilibrium, which is affected by the asymmetry of the interaction and the proportion of strong individuals. The stable equilibrium shows that strong individuals are willing to choose cooperation and weak individuals are willing to choose defection. In this case, the average frequency of cooperation is not less than the equilibrium frequency of cooperators with only symmetric interactions. In addition, complex interactions in spatially organized populations causes weak individuals to mimic the strategies of strong neighbors. Strong individuals with great benefit are willing to choose cooperation, and cooperators create a cluster with a core of strong cooperators and weak cooperators outside. For a wide range of parameters, the frequency of cooperation among weak individuals grows dramatically. Complex interactions frequently improves the frequency of cooperation while decreasing the frequency of cooperation slightly only over a narrow range of parameter. Because of the high frequency of cooperation, complex interactions can roughly solve the paradox in the snowdrift game.