Reputation incentives with public supervision promote cooperation in evolutionary games

Public supervision, as a source of social behavioral norms and moral guidelines, exerts important guidance and influence on individuals. To maintain public order, in this study, we propose a reputation incentives mechanism with public supervision, in which each player is granted the authority to evaluate others. These players, by observing, can make positive or negative evaluations that derive from the satisfaction level of the interactive behavior to neighbors choosing cooperation or defection in each round of the evolutionary game. Evaluations made by defectors are considered untrustworthy, resulting in the evaluation values assigned to others being halved. After mutual evaluation, the reputation is an average of the evaluations given by all their neighbors and then is consequently granted to each player. The results of numerical simulations demonstrate that reputation provides rewards that positively incentivize cooperation. And we observe that a weaker evaluation intensity leads to more stable and higher levels of cooperation among individuals. This mechanism provides valuable insights into the evolution of reputation and the optimization of supervising mechanisms.