Reputation in public goods cooperation under double Q-learning protocol

Abstract

Understanding and resolving cooperation dilemmas are key challenges in evolutionary game theory, which have revealed several mechanisms to address them. This paper investigates the comprehensive influence of multiple reputation-related components on public cooperation. In particular, cooperative investments in public goods game are not fixed but simultaneously depend on the reputation of group organizers and the population’s cooperation willingness, hence indirectly impacting on the players’ income. Additionally, individual payoff can also be directly affected by their reputation via a weighted approach which effectively evaluates the actual income of players. Unlike conventional models, the reputation change of players is non-monotonic, but may transform abruptly due to specific actions. Importantly, a theoretically supported double $Q$-learning algorithm is introduced to avoid overestimation bias inherent from the classical $Q$-learning algorithm. Our simulations reveal a significantly improved cooperation level, that is explained by a detailed $Q$-value analysis. We also observe the lack of massive cooperative clusters in the absence of network reciprocity. At the same time, as an intriguing phenomenon, some actors maintain moderate reputation and are continuously flipping between cooperation and defection. The robustness of our results are validated by mean-field approximation.