# Bayesian Opponent Exploitation in Imperfect-Information Games

arXiv: https://arxiv.org/abs/1603.03491 · HTML: https://mlsanity.com/paper/1603.03491/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Mar 2016.

## Built on by (most cited first, 4 of 4)

- [Deception in Social Learning: A Multi-Agent Reinforcement Learning Perspective](https://mlsanity.com/paper/2106.05402/) (2021)
- [Best of Both Worlds: Regret Minimization versus Minimax Play](https://mlsanity.com/paper/2502.11673/) (2025)
- [Opponent Modeling in Multiplayer Imperfect-Information Games](https://mlsanity.com/paper/2212.06027/) (2022)
- [Consistent Opponent Modeling in Imperfect-Information Games](https://mlsanity.com/paper/2508.17671/) (2025)

## Abstract (arXiv)

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.