Opponent Modeling in Multiplayer Imperfect-Information Games
Sam Ganzfried, Kevin A. Wang, Max Chiswick
TL;DR
In multiplayer imperfect-information games, computing equilibria is often intractable, and traditional Nash-based strategies ignore evolving opponent behavior. The paper introduces a domain-independent Bayesian opponent-modeling method that initializes from no history, samples opponent strategies from independent Dirichlet priors with means anchored to Nash equilibria, updates posteriors via observations, and switches to a best-response after a switch time $H$ using importance sampling to remain scalable. Key contributions include a principled prior and posterior update mechanism, a two-phase play scheme, and a complexity bound of $O((n-1)k^{n-1}|I|^n|A|^n)$, validated on three-player Kuhn poker against real agents and exact Nash strategies. The results show the method substantially outperforms Nash-based strategies, highlighting its ability to exploit weaker opponents while maintaining strong performance against stronger ones, with broad applicability to real-world multiplayer imperfect-information settings.
Abstract
In many real-world settings agents engage in strategic interactions with multiple opposing agents who can employ a wide variety of strategies. The standard approach for designing agents for such settings is to compute or approximate a relevant game-theoretic solution concept such as Nash equilibrium and then follow the prescribed strategy. However, such a strategy ignores any observations of opponents' play, which may indicate shortcomings that can be exploited. We present an approach for opponent modeling in multiplayer imperfect-information games where we collect observations of opponents' play through repeated interactions. We run experiments against a wide variety of real opponents and exact Nash equilibrium strategies in three-player Kuhn poker and show that our algorithm significantly outperforms all of the agents, including the exact Nash equilibrium strategies.