Evolutionary dynamics of strategies for threshold snowdrift games on complex networks

The puzzle of altruistic cooperation attracts many concerns of researchers in multiple subjects nowadays. In this work we establish punishment in the framework of a threshold multiple-player snowdrift game employed as the scenario for the cooperative dilemma problem. We show by analysis that given this assumption, punishing free riders can significantly influence the evolution dynamics, and the results are driven by the specific components of the punishing rule. Intriguingly larger thresholds of the game provide a more favorable scenario for the coexistence of the cooperators and defectors under a broad value range of parameters. Furthermore, we provide a two-layer network framework for describing the individual interactions, by extending the threshold snowdrift games to the double-layers networks. Here, cooperators are best supported on complex networks by applying the threshold, moreover, the interlinks between the two layers are conducive to reinforce the network reciprocity.