Unveiling the masks: Deception and reputation in spatial prisoner’s dilemma game

The topic of how to solve cooperation dilemma has been extensively investigated, and numerous mechanisms involved third-party identities have been proposed to promote cooperation level. This paper considers a more realistic strategy named pseudo-cooperation (PC) in the prisoner’s dilemma game, characterized by incomplete cooperation. Participants employing this strategy attempt to deceive others by superficial cooperation, thereby resulting in payoff increases when confronted with other strategies. Moreover, distinct strategic choices lead to dynamic changes in players’ reputation, which in turn directly influences their income. Specifically, the reputation is incorporated into part of individuals’ payoff rather than indirectly affecting them. Simulation experiments are respectively conducted in well-mixed and structured populations, and the results demonstrate that the reputation-based PC strategy significantly facilitates the emergence of cooperation behaviors in both environments. Furthermore, the criteria for the three types of players to emerge, vanish or dominate the system can be partially identified in well-mixed populations. Importantly, the region of high cooperation density in the square network is wider than those in well-mixed populations, which displays the positive role of network reciprocity.