Multigames with voluntary participation on interdependent networks and the evolution of cooperation

Multigames with voluntary participation and interdependent networks could facilitate cooperation from different perspectives. Motivated by the two mechanisms, we attempt to perform multigames voluntarily on interdependent networks and investigate the evolution of cooperation. In our work, the sucker's payoff could randomly split population on both networks into two types to play the Prisoner's Dilemma and Snowdrift respectively. Meanwhile, there are three strategies - cooperation, defection and going it alone - to choose. We show that the cooperation on both networks can be improved by the diversity of sucker's payoff and bias in the utility function for the smaller values of temptation to defect. Moreover, with the increasing of magnitude of sucker's payoff within a certain range, more cooperators emerge on both networks arising from spatial distribution of strategies. And a stronger bias in the utility function could promote cooperation on the main network, which is because of the fantastic network reciprocity caused by bias in the utility function. Besides, more players playing SD on one network is able to improve the cooperation on this network regardless of which type game to choose for players on the other network.