Computing Optimal Equilibria and Mechanisms via Learning in Zero-Sum Extensive-Form Games

Brian Hu Zhang, Gabriele Farina, Ioannis Anagnostides, Federico Cacciamani, Stephen Marcus McAleer, Andreas Alexander Haupt, Andrea Celli, Nicola Gatti, Vincent Conitzer, Tuomas Sandholm

Keywords: extensive-form games, deep reinforcement learning, mechanism design, correlated equilibria

TL;DR: We introduce a new scalable approach for computing optimal equilibria in games via a reduction to a zero-sum extensive-form game.

Abstract: We introduce a new approach for computing optimal equilibria via learning in games. It applies to extensive-form settings with any number of players, including mechanism design, information design, and solution concepts such as correlated, communication, and certification equilibria. We observe that optimal equilibria are minimax equilibrium strategies of a player in an extensive-form zero-sum game. This reformulation allows to apply techniques for learning in zero-sum games, yielding the first learning dynamics that converge to optimal equilibria, not only in empirical averages, but also in iterates. We demonstrate the practical scalability and flexibility of our approach by attaining state-of-the-art performance in benchmark tabular games, and by computing an optimal mechanism for a sequential auction design problem using deep reinforcement learning.

Submission Number: 13565