LOPT: Learning Optimal Pigovian Tax in Sequential Social Dilemmas

Multi-agent reinforcement learning (MARL) has emerged as a powerful framework for modeling autonomous agents that independently optimize their individual objectives. However, in mixed-motive MARL environments, rational self-interested behaviors often lead to collectively suboptimal outcomes situations commonly referred to as social dilemmas. A key challenge in addressing social dilemmas lies in accurately quantifying and representing them in a numerical form that captures how self-interested agent behaviors impact social welfare. To address this challenge, \textit{externalities} in the economic concept is adopted and extended to denote the unaccounted-for impact of one agent's actions on others, as a means to rigorously quantify social dilemmas.