Impact of keeping silence on spatial reciprocity in spatial games

In social systems, the purpose of individuals playing games is to get higher payoffs. However, if the benefit from game interactions does not achieve their expectation, agents may be more inclined to escape from games to reduce the potential consumption. Of particular interest, this trait could be mimicked by the so-called “silence” strategy. In this work, we consider silence strategy in the framework of prisoner’s dilemma game, where players either engage in the game as cooperators or defectors, or gain no any payoff as the silence agents. The events of turning into and escaping from silence strategy depend on both the consumption level and silence period. Of particular interest, it is unveiled that there exists an intermediate consumption level that could guarantee the optimal cooperation circumstance. For the small consumption level, the silence strategy could enhance the frequency of cooperation through the rock–scissor–paper cycle. While for the large consumption level, vast majority of players choose the silence strategy to avoid the high loss of engaging in games. This discovery is universally effective for the silence period.