Characteristics of the evolution of cooperation by the probabilistic peer-punishment based on the difference of payoff

Based on those findings, this study exhibits the characteristics of the evolution of cooperation by the proposed peer-punishment. Those characteristics present the significant contribution to knowledge that for the evolution of cooperation, a limited number of players should cause severe damage to defectors at the large expense of their payoff when connections between them are sparse, whereas a greater number of players should share the responsibility to punish defectors at the relatively small expense of their payoff when connections between them are dense.