Learning to Play General-Sum Games Against Multiple Boundedly Rational Agents

TL;DR

This paper introduces a reinforcement learning framework for training robust principals in multi-agent general-sum games, effectively handling worst-case responses and bounded rationality, demonstrated through mechanism design applications.

Contribution

It presents a novel RL-based approach that efficiently identifies worst-case agent responses in smooth games and extends to bounded rationality, improving robustness in multi-agent settings.

Findings

Learned robust mechanisms in matrix and spatiotemporal games

Achieved a 15% welfare improvement in a simulated economy

Demonstrated effectiveness against boundedly rational agents

Abstract

We study the problem of training a principal in a multi-agent general-sum game using reinforcement learning (RL). Learning a robust principal policy requires anticipating the worst possible strategic responses of other agents, which is generally NP-hard. However, we show that no-regret dynamics can identify these worst-case responses in poly-time in smooth games. We propose a framework that uses this policy evaluation method for efficiently learning a robust principal policy using RL. This framework can be extended to provide robustness to boundedly rational agents too. Our motivating application is automated mechanism design: we empirically demonstrate our framework learns robust mechanisms in both matrix games and complex spatiotemporal games. In particular, we learn a dynamic tax policy that improves the welfare of a simulated trade-and-barter economy by 15%, even when facing previously unseen boundedly rational RL taxpayers.