Spontaneous punishment promotes cooperation in public good game

Abstract

Abstract Punishment widely exists in social and biological systems and it has been proved to be an effective way to promote cooperation in evolutionary game in previous work. In this paper, we introduce a new mechanism of punishment that the punishment fine can be multiplied if there are several punishers decide to punish a defector, which leads to a low payoff of defector and promotes the level of cooperation. This mechanism can simulate group hunt which is common in natural animal world, for example, in biological system, a pack of animal in which every individual cooperates with each other can hunt a prey which is stronger than an individual inside the pack. This phenomenon can be explained by that the ability of punishment is multiplied by individuals cooperating with each other to carry out the punishment. A pack of wolves can make the process of hunt easier than the hunt implemented by a lone wolf, inspired by which we construct this mechanism of punishment to simulate the group punishment. Interestingly, we find that this mechanism can dramatically promotes the level of cooperation when we compare the simulation result with traditional evolutionary public good game. In order to figure out how our new mechanism of punishment promotes the cooperation, we have drawn several figures below to explain the mechanism. Our work simulates a widely existing phenomenon in biological and social systems and reveals some essential principles in the process of evolution.