A remarkable effect of the combination of probabilistic peer-punishment and coevolutionary mechanism on the evolution of cooperation

In the previous studies, the author has proposed the probabilistic peer-punishment based on the difference of payoff, and presented that the proposed peer-punishment utilizes its mechanism for preventing antisocial punishment like retaliation of a defector on a cooperator, effectively enhances the evolution of cooperation, and greatly increases the average payoff of all players in various parameters regarding static three types of topology of connections. Here, this study introduces both activities of breaking and creating connections of every player based on his/her preference to the model of the proposed peer-punishment. Every player will keep connections with his/her preferable players, whereas he/she will frequently break connections with his/her dissatisfied other players. Therefore, the new model of this study is the combination of probabilistic peer-punishment and coevolutionary mechanism that not only strategy of players but also connections between players evolve. This study discovers new knowledge that such combination induces high-level evolution of cooperation and great increase of the average payoff of all players in the condition where cooperation is hard to evolve.