Bayesian Opponent Exploitation in Imperfect-Information Games

TL;DR

This paper introduces the first exact polynomial-time algorithm for opponent exploitation in a natural class of imperfect-information games, improving over prior approximation methods and demonstrating practical efficiency.

Contribution

It presents the first exact algorithm for Bayesian opponent exploitation in certain imperfect-information games, advancing beyond previous approximate approaches.

Findings

Algorithm runs quickly in practice

Outperforms prior approximation methods

Effective for a natural class of imperfect-information games

Abstract

Two fundamental problems in computational game theory are computing a Nash equilibrium and learning to exploit opponents given observations of their play (opponent exploitation). The latter is perhaps even more important than the former: Nash equilibrium does not have a compelling theoretical justification in game classes other than two-player zero-sum, and for all games one can potentially do better by exploiting perceived weaknesses of the opponent than by following a static equilibrium strategy throughout the match. The natural setting for opponent exploitation is the Bayesian setting where we have a prior model that is integrated with observations to create a posterior opponent model that we respond to. The most natural, and a well-studied prior distribution is the Dirichlet distribution. An exact polynomial-time algorithm is known for best-responding to the posterior distribution for an opponent assuming a Dirichlet prior with multinomial sampling in normal-form games; however, for imperfect-information games the best known algorithm is based on approximating an infinite integral without theoretical guarantees. We present the first exact algorithm for a natural class of imperfect-information games. We demonstrate that our algorithm runs quickly in practice and outperforms the best prior approaches. We also present an algorithm for the uniform prior setting.