Learning Optimal “Pigovian Tax” in Sequential Social Dilemmas

In multi-agent reinforcement learning (MARL), each agent acts to maximize its individual accumulated rewards. Nevertheless, individual accumulated rewards could not fully reflect how others perceive them, resulting in selfish behaviors that undermine global performance, which brings the social dilemmas. This paper adapt the famous externality theory in economic area to analyze social dilemmas in MARL, and propose the method called Learning Optimal Pigovian Tax (LOPT) to internalize the externalities in MARL. Furthermore, a reward shaping mechanism based on the approximated optimal “Pigovian Tax” is applied to reduce the social cost of each agent and tries to alleviate the social dilemmas. Compared with existing state-of-the-art methods, the proposed LOPT leads to higher collective social welfare in both the Escape Room and the Cleanup environments, which shows the superiority of our method in solving social dilemmas.