A proportional-neighborhood-diversity evolution in snowdrift game on square lattice

Abstract

The subject of how to facilitate cooperation of evolution through different mechanisms has been intensively investigated. For snowdrift game, researches have shown that a moderate dilution of the number of neighbors of individuals will benefit the evolution of cooperation, and have not shown how different dilution degrees effect evolution of cooperation. This paper proposes a proportional-neighborhood-diversity (PND) mechanism which takes into account some relatively typical situations. The core lies in: We provide a proportional vector to indicate the proportion of individuals with different number of interactive neighbors. Each player has fixed spatial neighbors and only plays with interactive neighbors selected from its spatial neighbors. This study is performed by means of the Monte Carlo method and an extended pair-approximation method. The Monte Carlo simulation results show that, compared with the traditional case, introducing different dilution degrees in evolution promotes the emergence of cooperative behavior. An interesting phenomenon is that when most individuals have a smaller number of interactive neighbors, the cooperation level is relatively higher. When applied to the evolutionary game, the PND mechanism can reduce game cost since the number of interactive neighbors is less than that of fixed neighbors in whole evolutionary process. Moreover, it has potential role in social management since the proposed mechanism is more realistic.