Evolution of cooperation in the public goods game with Q-learning

Abstract: Recent paradigm shifts from imitation learning to reinforcement learning (RL) is shown to be productive in understanding human behaviors. In the RL paradigm, individuals search for optimal strategies through interaction with the environment to make decisions. This implies that gathering, processing, and utilizing information from their surroundings are crucial. However, existing studies typically study pairwise games such as the prisoners' dilemma and employ a self-regarding setup, where individuals play against one opponent based solely on their own strategies, neglecting the environmental information. In this work, we investigate the evolution of cooperation with the multiplayer game -- the public goods game using the Q-learning algorithm by leveraging the environmental information. Specifically, the decision-making of players is based upon the cooperation information in their neighborhood. Our results show that cooperation is more likely to emerge compared to the case of imitation learning by using Fermi rule. Of particular interest is the observation of an anomalous non-monotonic dependence which is revealed when voluntary participation is further introduced. The analysis of the Q-table explains the mechanisms behind the cooperation evolution. Our findings indicate the fundamental role of environment information in the RL paradigm to understand the evolution of cooperation, and human behaviors in general.