Influence of bolstering network reciprocity in the evolutionary spatial Prisoner's Dilemma game: a perspective

Many recent studies on evolutionary spatial Prisoner's Dilemma (SPD) games have provided insights into the mechanisms and frameworks that bolster the effect of network reciprocity. In this article, we provide a concise and comprehensive review of previous studies on evolutionary games and network reciprocity. Subsequently, we evaluate and compare the results from such studies in a unified manner to answer an open question in evolutionary SPD games: What are the factors underlying network reciprocity and what effect do these factors have on the emergence and promotion of cooperation? As a first step, we introduce a novel indicator to quantitatively evaluate the effectiveness (contribution) of a final fraction of cooperators via the introduction of the associated mechanisms into a simple evolutionary SPD game. In this game, the players are located on a two-dimensional square lattice with the Moore neighborhood and update their strategies by imitating the strategy of the best performing player among their neighbors, and the dynamics are separated into two periods: the enduring (END) period and the expanding (EXP) period. The initial fraction of cooperators is decreased transiently via the invasion and exploitation of defectors in the END period, and over the period, the fraction of cooperators is increased to expand cooperative clusters in the EXP period. Moreover, we also evaluate the statistical validity of our indicator by performing regression analyses. Our results indicate that two factors bolster the effect of network reciprocity: (1) the shape of the cooperative cluster (C-cluster) formed in the END period and (2) the ability to expand a single perfect C-cluster, which is the smallest patch, to increase the opportunity for interactions between cooperators and defectors and reduce exploitation by defectors in the EXP period.