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. Based on this measurement, a novel method, \textbf{L}earning \textbf{O}ptimal \textbf{P}igovian \textbf{T}ax (\textbf{LOPT}) is proposed. Inspired by Pigovian taxes, which are designed to internalize externalities by imposing cost on negative societal impacts, LOPT employs an auxiliary tax agent that learns an optimal Pigovian tax policy to reshape individual rewards aligned with social welfare, thereby promoting agent coordination and mitigating social dilemmas. We support LOPT with theoretical analysis and validate it on standard MARL benchmarks, including Escape Room and Cleanup. Results show that by effectively internalizing externalities that quantify social dilemmas, LOPT aligns individual objectives with collective goals, significantly improving social welfare over state-of-the-art baselines.