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Subgame solving is a technique for scaling algorithms to large games by locally refining a precomputed blueprint strategy during gameplay. While straightforward in perfect-information games where search starts from the current state,…

Computer Science and Game Theory · Computer Science 2026-01-27 Ondrej Kubicek , Viliam Lisy , Tuomas Sandholm

While Nash equilibrium has emerged as the central game-theoretic solution concept, many important games contain several Nash equilibria and we must determine how to select between them in order to create real strategic agents. Several Nash…

Computer Science and Game Theory · Computer Science 2024-04-30 Sam Ganzfried

Equilibrium finding in two-player zero-sum games with perfect recall is a well-studied topic that has led to many breakthroughs in computational game theory. This paper aims to generalize such techniques to (timeable) two-player zero-sum…

Computer Science and Game Theory · Computer Science 2026-05-05 Luca Carminati , Brian Hu Zhang , Federico Cacciamani , Junkang Li , Gabriele Farina , Nicola Gatti , Tuomas Sandholm

In this paper we investigate the Follow the Regularized Leader dynamics in sequential imperfect information games (IIG). We generalize existing results of Poincar\'e recurrence from normal-form games to zero-sum two-player imperfect…

Recently, AlphaZero has achieved landmark results in deep reinforcement learning, by providing a single self-play architecture that learned three different games at super human level. AlphaZero is a large and complicated system with many…

Artificial Intelligence · Computer Science 2021-01-11 Hui Wang , Mike Preuss , Aske Plaat

Creating strong agents for games with more than two players is a major open problem in AI. Common approaches are based on approximating game-theoretic solution concepts such as Nash equilibrium, which have strong theoretical guarantees in…

Computer Science and Game Theory · Computer Science 2018-11-07 Sam Ganzfried , Austin Nowak , Joannier Pinales

Poker is an imperfect information game that has served as a long-standing benchmark for decision-making under uncertainty. To maximize utility beyond the Nash equilibrium, an agent can deviate from Nash-equilibrium policies to exploit…

Machine Learning · Computer Science 2026-05-12 Vlad Murgoci , Matthijs Spaan , Yaniv Oren

Reinforcement learning from self-play has recently reported many successes. Self-play, where the agents compete with themselves, is often used to generate training data for iterative policy improvement. In previous work, heuristic rules are…

Machine Learning · Computer Science 2020-09-15 Yuanyi Zhong , Yuan Zhou , Jian Peng

In the last years, the DeepMind algorithm AlphaZero has become the state of the art to efficiently tackle perfect information two-player zero-sum games with a win/lose outcome. However, when the win/lose outcome is decided by a final score…

Artificial Intelligence · Computer Science 2023-01-10 Luca Pasqualini , Gianluca Amato , Marco Fantozzi , Rosa Gini , Alessandro Marchetti , Carlo Metta , Francesco Morandin , Maurizio Parton

Search in test time is often used to improve the performance of reinforcement learning algorithms. Performing theoretically sound search in fully adversarial two-player games with imperfect information is notoriously difficult and requires…

Computer Science and Game Theory · Computer Science 2025-01-30 Ondrej Kubicek , Neil Burch , Viliam Lisy

Extensive-form games are a common model for multiagent interactions with imperfect information. In two-player zero-sum games, the typical solution concept is a Nash equilibrium over the unconstrained strategy set for each player. In many…

Computer Science and Game Theory · Computer Science 2019-02-07 Trevor Davis , Kevin Waugh , Michael Bowling

The goal of agents in multi-agent environments is to maximize total reward against the opposing agents that are encountered. Following a game-theoretic solution concept, such as Nash equilibrium, may obtain a strong performance in some…

Computer Science and Game Theory · Computer Science 2026-01-05 Sam Ganzfried

A fundamental challenge in imperfect-information games is that states do not have well-defined values. As a result, depth-limited search algorithms used in single-agent settings and perfect-information games do not apply. This paper…

Computer Science and Game Theory · Computer Science 2018-05-23 Noam Brown , Tuomas Sandholm , Brandon Amos

Imperfect-information multiplayer games test whether agents can act under hidden information, sparse rewards, and non-stationary opponents. We study these challenges in Big 2, a four-player imperfect-information card game. We develop a…

Machine Learning · Computer Science 2026-05-29 Aalok Patwa

This paper proposes new, end-to-end deep reinforcement learning algorithms for learning two-player zero-sum Markov games. Different from prior efforts on training agents to beat a fixed set of opponents, our objective is to find the Nash…

Machine Learning · Computer Science 2023-03-08 Zihan Ding , Dijia Su , Qinghua Liu , Chi Jin

Search has played a fundamental role in computer game research since the very beginning. And while online search has been commonly used in perfect information games such as Chess and Go, online search methods for imperfect information games…

Computer Science and Game Theory · Computer Science 2021-03-03 Michal Šustr , Martin Schmid , Matej Moravčík , Neil Burch , Marc Lanctot , Michael Bowling

An imperfect-information game is a type of game with asymmetric information. It is more common in life than perfect-information game. Artificial intelligence (AI) in imperfect-information games, such like poker, has made considerable…

Artificial Intelligence · Computer Science 2024-05-29 Qibin Zhou , Dongdong Bai , Junge Zhang , Fuqing Duan , Kaiqi Huang

Secure equilibrium is a refinement of Nash equilibrium, which provides some security to the players against deviations when a player changes his strategy to another best response strategy. The concept of secure equilibrium is specifically…

Computer Science and Game Theory · Computer Science 2014-05-08 Julie De Pril , János Flesch , Jeroen Kuipers , Gijs Schoenmakers , Koos Vrieze

Researchers on artificial intelligence have achieved human-level intelligence in large-scale perfect-information games, but it is still a challenge to achieve (nearly) optimal results (in other words, an approximate Nash Equilibrium) in…

Artificial Intelligence · Computer Science 2019-04-09 Li Zhang , Wei Wang , Shijian Li , Gang Pan

The AlphaZero algorithm for the learning of strategy games via self-play, which has produced superhuman ability in the games of Go, chess, and shogi, uses a quantitative reward function for game outcomes, requiring the users of the…

Machine Learning · Computer Science 2019-12-17 Dan Schmidt , Nick Moran , Jonathan S. Rosenfeld , Jonathan Rosenthal , Jonathan Yedidia