Get It in Writing: Formal Contracts Mitigate Social Dilemmas in Multi-Agent RL

Multi-agent reinforcement learning (MARL) is a powerful tool for training automated systems 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 state-dependent 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 observed Markov games exhibit socially optimal behavior, given a sufficiently rich space of contracts. Next, we complement our game-theoretic analysis by showing that state-of-the-art RL algorithms learn socially optimal policies given our augmentation. Our experiments include classic static dilemmas like Stag Hunt, Prisoner's Dilemma and a public goods game, as well as dynamic interactions that simulate traffic, pollution management and common pool resource management.