Multiplicative Weight Update with Mutation in Two-Player Zero-Sum Extensive-Form Games

Abstract

In this study, we propose a multiplicative weight update algorithm that utilizes mutations in two-player zero-sum extensive-form games. These games are important models for decision-making under imperfect information. While equilibria in these games can be computed using linear programming, it becomes challenging to handle large-scale games such as poker. To address this issue, learning algorithms for finding an (approximate) equilibrium have been proposed. However, most of the existing algorithms converge to Nash equilibrium through time-averaged strategies. In normal-form games, it has been shown that introducing mutations allows for learning equilibrium strategies without taking time averages. Inspired by that, we propose the Dilated Mutant Multiplicative Weight Update with the introduction of mutations in extensive-form games. The experimental results show that the proposed method can learn equilibrium strategies without computing time averages for multiple settings.