Regarding costly punishment of two types, especially peer-punishment is considered to decrease the average payoff of all players as well as pool-punishment does, and to facilitate the antisocial punishment as a result of natural selection. To solve those problems, the author has proposed the probabilistic peer-punishment based on the difference of payoff. In the limited condition, the proposed peer-punishment has shown the positive effects on the evolution of cooperation, and increased the average payoff of all players.
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.
Characteristics of the evolution of cooperation by the probabilistic peer-punishment based on the difference of payoff
Chaos, Solitons & Fractals
Volume 95, February 2017, Pages 77–83