Multigames with social punishment and the evolution of cooperation

Both the strategy social punishment defined as the special cooperation and playing multigames could lead to the enhancement of cooperation in social dilemmas. To take this into consideration, we introduce multigames with social punishment and investigate the evolution of cooperation. In our work, the population is randomly divided into two types. Players of type A, whose proportion is v, adopt a negative value of the sucker's payoff to play the Prisoner's Dilemma (PD), while players of type B, whose proportion is 1−v, adopt a positive value to play Snowdrift (SD). Meanwhile, three strategies can be selected, including cooperation, defection, and punishment. We show that for the larger temptation to defect, the cooperation can be enhanced by the diversity of sucker's payoff. In addition, when the contribution of sucker's payoff is larger or less players choose to play PD, the cooperators become more dominated, which can be explained by the special spatial distribution of the two types of players.