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This work investigates the adaptation of the AlphaZero reinforcement learning algorithm to Tablut, an asymmetric historical board game featuring unequal piece counts and distinct player objectives (king capture versus king escape). While…

Machine Learning · Computer Science 2026-04-08 Tõnis Lees , Tambet Matiisen

We consider extensive games with perfect information with well-founded game trees and study the problems of existence and of characterization of the sets of subgame perfect equilibria in these games. We also provide such characterizations…

Computer Science and Game Theory · Computer Science 2021-06-23 Krzysztof R. Apt , Sunil Simon

Reinforcement Learning (RL) has been widely used in many applications, particularly in gaming, which serves as an excellent training ground for AI models. Google DeepMind has pioneered innovations in this field, employing reinforcement…

Artificial Intelligence · Computer Science 2026-02-12 Abdelrhman Shaheen , Anas Badr , Ali Abohendy , Hatem Alsaadawy , Nadine Alsayad , Ehab H. El-Shazly

Repeated games consider a situation where multiple agents are motivated by their independent rewards throughout learning. In general, the dynamics of their learning become complex. Especially when their rewards compete with each other like…

Computer Science and Game Theory · Computer Science 2023-05-23 Yuma Fujimoto , Kaito Ariu , Kenshi Abe

Self-play, a learning paradigm where agents iteratively refine their policies by interacting with historical or concurrent versions of themselves or other evolving agents, has shown remarkable success in solving complex non-cooperative…

Artificial Intelligence · Computer Science 2025-10-21 Ruize Zhang , Zelai Xu , Chengdong Ma , Chao Yu , Wei-Wei Tu , Wenhao Tang , Shiyu Huang , Deheng Ye , Wenbo Ding , Yaodong Yang , Yu Wang

Games have a long history as benchmarks for progress in artificial intelligence. Approaches using search and learning produced strong performance across many perfect information games, and approaches using game-theoretic reasoning and…

Limited lookahead has been studied for decades in perfect-information games. We initiate a new direction via two simultaneous deviation points: generalization to imperfect-information games and a game-theoretic approach. We study how one…

Computer Science and Game Theory · Computer Science 2020-03-20 Christian Kroer , Tuomas Sandholm

Decomposition, i.e. independently analyzing possible subgames, has proven to be an essential principle for effective decision-making in perfect information games. However, in imperfect information games, decomposition has proven to be…

Computer Science and Game Theory · Computer Science 2014-04-22 Neil Burch , Michael Johanson , Michael Bowling

Counterfactual Regret Minimization (CFR) is the most successful algorithm for finding approximate Nash equilibria in imperfect information games. However, CFR's reliance on full game-tree traversals limits its scalability. For this reason,…

Computer Science and Game Theory · Computer Science 2019-10-07 Eric Steinberger

We study the problem of learning in zero-sum matrix games with repeated play and bandit feedback. Specifically, we focus on developing uncoupled algorithms that guarantee, without communication between players, the convergence of the…

Machine Learning · Computer Science 2026-04-20 Côme Fiegel , Pierre Ménard , Tadashi Kozuno , Michal Valko , Vianney Perchet

We present efficient algorithms for computing optimal or approximately optimal strategies in a zero-sum game for which Player I has n pure strategies and Player II has an arbitrary number of pure strategies. We assume that for any given…

Optimization and Control · Mathematics 2018-06-21 Lisa Hellerstein , Thomas Lidbetter , Daniel Pirutinsky

Robust Reinforcement Learning (RRL) is a promising Reinforcement Learning (RL) paradigm aimed at training robust to uncertainty or disturbances models, making them more efficient for real-world applications. Following this paradigm,…

Machine Learning · Computer Science 2024-05-06 Anton Plaksin , Vitaly Kalev

Reinforcement Learning Algorithms (RLA) are useful machine learning tools to understand how decision makers react to signals. It is known that RLA converge towards the pure Nash Equilibria (NE) of finite congestion games and more generally,…

Computer Science and Game Theory · Computer Science 2021-11-15 Benoît Sohet , Yezekael Hayel , Olivier Beaude , Alban Jeandin

There have been extensive studies on learning in zero-sum games, focusing on the analysis of the existence and algorithmic convergence of Nash equilibrium (NE). Existing studies mainly focus on symmetric games where the strategy spaces of…

Computer Science and Game Theory · Computer Science 2025-02-11 Yuheng Li , Panpan Wang , Haipeng Chen

The task of computing approximate Nash equilibria in large zero-sum extensive-form games has received a tremendous amount of attention due mainly to the Annual Computer Poker Competition. Immediately after its inception, two competing and…

Artificial Intelligence · Computer Science 2014-11-19 Kevin Waugh , J. Andrew Bagnell

Algorithm design and analysis is a cornerstone of computer science, but it confronts a major challenge. Proving an algorithm's performance guarantee across all inputs has traditionally required extensive and often error-prone human effort.…

Computer Science and Game Theory · Computer Science 2025-08-19 Hanyu Li , Dongchen Li , Xiaotie Deng

Studying games in the complete information model makes them analytically tractable. However, large $n$ player interactions are more realistically modeled as games of incomplete information, where players may know little to nothing about the…

Computer Science and Game Theory · Computer Science 2015-12-11 Ryan Rogers , Aaron Roth

Nash equilibrium is a popular solution concept for solving imperfect-information games in practice. However, it has a major drawback: it does not preclude suboptimal play in branches of the game tree that are not reached in equilibrium.…

Computer Science and Game Theory · Computer Science 2017-05-29 Christian Kroer , Gabriele Farina , Tuomas Sandholm

Test-time reasoning significantly enhances pre-trained AI agents' performance. However, it requires an explicit environment model, often unavailable or overly complex in real-world scenarios. While MuZero enables effective model learning…

Artificial Intelligence · Computer Science 2025-10-07 Ondřej Kubíček , Viliam Lisý

Deep learning has achieved remarkable successes in solving challenging reinforcement learning (RL) problems when dense reward function is provided. However, in sparse reward environment it still often suffers from the need to carefully…

Machine Learning · Computer Science 2019-02-19 Hao Liu , Alexander Trott , Richard Socher , Caiming Xiong