Computing equilibria by incorporating qualitative models

Abstract

We present a new procedure for solving large games of imperfect information. Our approach involves---somewhat counterintuitively---solving an infinite approximation of the original game, then mapping the equilibrium to a strategy profile in the original game. Our main algorithm exploits some qualitative model of equilibrium structure as an additional input to find an equilibrium in continuous games. We prove that our approach is correct even if given a set of qualitative models (satisfying a technical property) of which only some are accurate. We compute equilibria in several classes of games for which no prior algorithms have been developed. In the course of our analysis, we also develop the first mixed-integer programming formulations for computing an epsilon-equilibrium in general multiplayer normal and extensive-form games based on the extension of our initial algorithm to the multiplayer setting, which may be of independent interest. Experiments suggest that our approach can outperform the prior state of the art, abstraction-based approaches. In addition, we demonstrate the effectiveness of our main algorithm on a subgame of limit Texas hold'em---the most studied imperfect-information game in computer science.