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There has been significant recent progress in algorithms for approximation of Nash equilibrium in large two-player zero-sum imperfect-information games and exact computation of Nash equilibrium in multiplayer strategic-form games. While…

Computer Science and Game Theory · Computer Science 2025-10-01 Sam Ganzfried

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

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

We explore the power of semidefinite programming (SDP) for finding additive $epsilon$-approximate Nash equilibria in bimatrix games. We introduce an SDP relaxation for a quadratic programming formulation of the Nash equilibrium (NE) problem…

Optimization and Control · Mathematics 2019-08-16 Amir Ali Ahmadi , Jeffrey Zhang

We propose a new globally convergent stochastic second order method. Our starting point is the development of a new Sketched Newton-Raphson (SNR) method for solving large scale nonlinear equations of the form $F(x)=0$ with $F:\mathbb{R}^p…

Numerical Analysis · Mathematics 2022-05-10 Rui Yuan , Alessandro Lazaric , Robert M. Gower

We design a distributed algorithm to seek generalized Nash equilibria of a robust game with uncertain coupled constraints. Due to the uncertainty of parameters in set constraints, we aim to find a generalized Nash equilibrium in the worst…

Optimization and Control · Mathematics 2022-04-05 Gehui Xu , Guanpu Chen , Hongsheng Qi

In this paper we propose a numerical method to obtain an approximation of Nash equilibria for multi-player non-cooperative games with a special structure. We consider the infinite horizon problem in a case which leads to a system of…

Numerical Analysis · Mathematics 2016-02-19 Simone Cacace , Emiliano Cristiani , Maurizio Falcone

We study reinforcement learning for two-player zero-sum Markov games with simultaneous moves in the finite-horizon setting, where the transition kernel of the underlying Markov games can be parameterized by a linear function over the…

Machine Learning · Computer Science 2022-04-21 Zixiang Chen , Dongruo Zhou , Quanquan Gu

We study the problem of computing an $\epsilon$-approximate Nash equilibrium of a two-player, bilinear game with a bounded payoff matrix $A \in \mathbb{R}^{m \times n}$, when the players' strategies are constrained to lie in simple sets. We…

Optimization and Control · Mathematics 2026-01-08 Ishani Karmarkar , Liam O'Carroll , Aaron Sidford

This work proposes a novel distributed approach for computing a Nash equilibrium in convex games with restricted strongly monotone pseudo-gradients. By leveraging the idea of the centralized operator extrapolation method presented in [4] to…

Optimization and Control · Mathematics 2023-10-25 Tatiana Tatarenko , Angelia Nedich

We propose a framework to compute approximate Nash equilibria in integer programming games with nonlinear payoffs, i.e., simultaneous and non-cooperative games where each player solves a parametrized mixed-integer nonlinear program. We…

Optimization and Control · Mathematics 2025-08-04 Aloïs Duguet , Margarida Carvalho , Gabriele Dragotto , Sandra Ulrich Ngueveu

In zero-sum games, the optimal strategy is well-defined by the Nash equilibrium. However, it is overly conservative when playing against suboptimal opponents and it can not exploit their weaknesses. Limited look-ahead game solving in…

Computer Science and Game Theory · Computer Science 2024-04-04 David Milec , Ondřej Kubíček , Viliam Lisý

The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as…

Optimization and Control · Mathematics 2016-09-27 Xiantao Xiao , Yongfeng Li , Zaiwen Wen , Liwei Zhang

Nash equilibrium is one of the most influential solution concepts in game theory. With the development of computer science and artificial intelligence, there is an increasing demand on Nash equilibrium computation, especially for Internet…

Computer Science and Game Theory · Computer Science 2023-12-19 Hanyu Li , Wenhan Huang , Zhijian Duan , David Henry Mguni , Kun Shao , Jun Wang , Xiaotie Deng

Nash equilibrium is perhaps the best-known solution concept in game theory. Such a solution assigns a strategy to each player which offers no incentive to unilaterally deviate. While a Nash equilibrium is guaranteed to always exist, the…

Computer Science and Game Theory · Computer Science 2025-04-29 David Sychrovský , Christopher Solinas , Revan MacQueen , Kevin Wang , James R. Wright , Nathan R. Sturtevant , Michael Bowling

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum…

Machine Learning · Computer Science 2020-04-06 Adrian Rivera Cardoso , Jacob Abernethy , He Wang , Huan Xu

The Nash Equilibrium (NE), one of the elegant and fundamental concepts in game theory, plays a crucial part within various fields, including engineering and computer science. However, efficiently computing an NE in normal-form games remains…

Optimization and Control · Mathematics 2025-04-01 Jianing Chen

We present a new methodology for computing approximate Nash equilibria for two-person non-cooperative games based upon certain extensions and specializations of an existing optimization approach previously used for the derivation of fixed…

Computer Science and Game Theory · Computer Science 2009-09-28 Haralampos Tsaknakis , Paul G. Spirakis

We study the problem of learning Nash equilibria in offline two-player zero-sum Markov games. While existing approaches often rely on explicit pessimism to address distribution shift, we show that KL regularization alone suffices to…

Machine Learning · Computer Science 2026-05-14 Claire Chen , Yuheng Zhang , Xinyu Liu , Zixuan Xie , Shuze Daniel Liu , Nan Jiang

We give a quantum algorithm for computing an $\epsilon$-approximate Nash equilibrium of a zero-sum game in a $m \times n$ payoff matrix with bounded entries. Given a standard quantum oracle for accessing the payoff matrix our algorithm runs…

Quantum Physics · Physics 2023-01-11 Adam Bouland , Yosheb Getachew , Yujia Jin , Aaron Sidford , Kevin Tian