Reputation-based probabilistic punishment on the evolution of cooperation in the spatial public goods game

Low-reputation defectors are more likely to be punished than defectors with high reputations. Motivated by this reality, this paper proposes a new mechanism, the reputation-based probabilistic punishment, into the spatial public goods game model. In this mechanism, players with time-dependent reputations are divided into two types, good players with reputations higher than the reputation threshold and bad players with reputations lower than the threshold. A defector considered a good player is less likely to be punished than a defector considered a bad player. Based on these assumptions, we systematically explore how this mechanism influences the evolution of cooperation. Through extensive simulations, we verify that a higher value of the reputation threshold is more conducive to promoting and maintaining cooperation. Moreover, increasing the cost of being punished could effectively encourage players to take cooperative behaviors. Simulation results show that both increasing the punishment intensity and increasing the punishment fine could increase the cost of being punished and are beneficial to the promotion of cooperation. Additionally, in the structured population, the distributions of strategies, reputation, and payoff in the evolutionary stable state are mainly present in the form of clusters.