Formal Contracts Mitigate Social Dilemmas in Multi-Agent RL
Andreas A. Haupt, Phillip J. K. Christoffersen, Mehul Damani, Dylan Hadfield-Menell
TL;DR
Social dilemmas in MARL arise when individual incentives misalign with collective welfare. The authors introduce Formal Contracting, augmenting Markov games with binding, state-dependent reward transfers governed by contractible observations, enabling agents to commit to socially beneficial outcomes. They prove that, with sufficiently expressive contract spaces, every subgame-perfect equilibrium attains socially optimal welfare in fully observable settings, and that greater expressiveness raises welfare under partial observability; they further propose MOCA to stabilize contract learning and demonstrate effectiveness across static and dynamic domains. The work also connects contracting to DEC-POMDPs under history-transparency and highlights the necessity of arbitrary unconditional transfers for welfare gains. Overall, it provides a principled mechanism to induce cooperation among selfish agents and offers scalable learning strategies for contract design in diverse MARL environments.
Abstract
Multi-agent Reinforcement Learning (MARL) is a powerful tool for training autonomous agents acting independently in a common environment. However, it can lead to sub-optimal behavior when individual incentives and group incentives diverge. Humans are remarkably capable at solving these social dilemmas. It is an open problem in MARL to replicate such cooperative behaviors in selfish agents. In this work, we draw upon the idea of formal contracting from economics to overcome diverging incentives between agents in MARL. We propose an augmentation to a Markov game where agents voluntarily agree to binding transfers of reward, under pre-specified conditions. Our contributions are theoretical and empirical. First, we show that this augmentation makes all subgame-perfect equilibria of all Fully Observable Markov Games exhibit socially optimal behavior, given a sufficiently rich space of contracts. Next, we show that for general contract spaces, and even under partial observability, richer contract spaces lead to higher welfare. Hence, contract space design solves an exploration-exploitation tradeoff, sidestepping incentive issues. We complement our theoretical analysis with experiments. Issues of exploration in the contracting augmentation are mitigated using a training methodology inspired by multi-objective reinforcement learning: Multi-Objective Contract Augmentation Learning (MOCA). We test our methodology in static, single-move games, as well as dynamic domains that simulate traffic, pollution management and common pool resource management.