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Related papers: Smoothed Complexity of 2-player Nash Equilibria

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We study the sample complexity of identifying the pure strategy Nash equilibrium (PSNE) in a two-player zero-sum matrix game with noise. Formally, we are given a stochastic model where any learner can sample an entry $(i,j)$ of the input…

Machine Learning · Computer Science 2023-11-29 Arnab Maiti , Ross Boczar , Kevin Jamieson , Lillian J. Ratliff

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

In their seminal work, Nayyar et al. (2013) showed that imperfect information can be abstracted away from common-payoff games by having players publicly announce their policies as they play. This insight underpins sound solvers and…

Computer Science and Game Theory · Computer Science 2023-08-02 Samuel Sokota , Ryan D'Orazio , Chun Kai Ling , David J. Wu , J. Zico Kolter , Noam Brown

In this work, we present a novel characterization of approximate Nash equilibria in a class of convex games over the simplex. To achieve this, we regularize the utility functions using the Shannon entropy term, connect the solutions to the…

Optimization and Control · Mathematics 2025-07-18 Tatiana Tatarenko , S. Rasoul Etesami

This paper introduces a new method to achieve stable convergence to Nash equilibrium in duopoly noncooperative games. Inspired by the recent fixed-time Nash Equilibrium seeking (NES) as well as prescribed-time extremum seeking (ES) and…

Optimization and Control · Mathematics 2024-05-27 Victor Hugo Pereira Rodrigues , Tiago Roux Oliveira , Miroslav Krstić , Tamer Başar

We consider the problem of computing mixed Nash equilibria of two-player zero-sum games with continuous sets of pure strategies and with first-order access to the payoff function. This problem arises for example in game-theory-inspired…

Optimization and Control · Mathematics 2025-09-04 Guillaume Wang , Lénaïc Chizat

We prove for every $n\ge4$ the existence of an $n$-player game in normal form with integer payoffs that has a unique Nash equilibrium, which is fully mixed. In the equilibrium, each probability weight is an algebraic number of degree…

Computer Science and Game Theory · Computer Science 2026-05-27 Edan Orzech , Martin Rinard

Many efficient algorithms have been designed to recover Nash equilibria of various classes of finite games. Special classes of continuous games with infinite strategy spaces, such as polynomial games, can be solved by semidefinite…

Computer Science and Game Theory · Computer Science 2020-10-01 Lukáš Adam , Rostislav Horčík , Tomáš Kasl , Tomáš Kroupa

We consider a class of hierarchical noncooperative $N$-player games where the $i$th player solves a parametrized stochastic mathematical program with equilibrium constraints (MPEC) with the caveat that the implicit form of the $i$th…

Optimization and Control · Mathematics 2022-02-23 Shisheng Cui , Uday V. Shanbhag

We propose local symplectic surgery, a two-timescale procedure for finding local Nash equilibria in two-player zero-sum games. We first show that previous gradient-based algorithms cannot guarantee convergence to local Nash equilibria due…

Machine Learning · Computer Science 2019-01-28 Eric V. Mazumdar , Michael I. Jordan , S. Shankar Sastry

We consider multi-agent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we…

Optimization and Control · Mathematics 2018-10-16 Tatiana Tatarenko , Maryam Kamgarpour

In this paper, we aim to design a distributed approximate algorithm for seeking Nash equilibria of an aggregative game. Due to the local set constraints of each player, projectionbased algorithms have been widely employed for solving such…

Optimization and Control · Mathematics 2021-08-30 Gehui Xu , Guanpu Chen , Hongsheng Qi , Yiguang Hong

PPAD refers to a class of computational problems for which solutions are guaranteed to exist due to a specific combinatorial principle. The most well-known such problem is that of computing a Nash equilibrium of a game. Other examples…

Computer Science and Game Theory · Computer Science 2015-03-19 Paul W. Goldberg

The proper equilibrium, introduced by Myerson (1978), is a classic refinement of the Nash equilibrium that has been referred to as the "mother of all refinements." For normal-form games, computing a proper equilibrium is known to be…

Computer Science and Game Theory · Computer Science 2026-02-11 Brian Hu Zhang , Ioannis Anagnostides , Kiriaki Fragkia , Maria-Florina Balcan , Tuomas Sandholm

We devise a policy-iteration algorithm for deterministic two-player discounted and mean-payoff games, that runs in polynomial time with high probability, on any input where each payoff is chosen independently from a sufficiently random…

Computer Science and Game Theory · Computer Science 2024-02-07 Bruno Loff , Mateusz Skomra

We consider polymatrix coordination games with individual preferences where every player corresponds to a node in a graph who plays with each neighbor a separate bimatrix game with non-negative symmetric payoffs. In this paper, we study…

Computer Science and Game Theory · Computer Science 2015-04-29 Mona Rahn , Guido Schäfer

We propose to smooth out the calibration score, which measures how good a forecaster is, by combining nearby forecasts. While regular calibration can be guaranteed only by randomized forecasting procedures, we show that smooth calibration…

Theoretical Economics · Economics 2022-10-14 Dean P. Foster , Sergiu Hart

Strategic interactions can be represented more concisely, and analyzed and solved more efficiently, if we are aware of the symmetries within the multiagent system. Symmetries also have conceptual implications, for example for equilibrium…

Computer Science and Game Theory · Computer Science 2025-03-03 Emanuel Tewolde , Brian Hu Zhang , Caspar Oesterheld , Tuomas Sandholm , Vincent Conitzer

An open problem in linear quadratic (LQ) games has been characterizing the Nash equilibria. This problem has renewed relevance given the surge of work on understanding the convergence of learning algorithms in dynamic games. This paper…

Computer Science and Game Theory · Computer Science 2025-04-18 Giulio Salizzoni , Reda Ouhamma , Maryam Kamgarpour

A long-standing open problem in algorithmic game theory asks whether or not there is a polynomial time algorithm to compute a Nash equilibrium in a random bimatrix game. We study random win-lose games, where the entries of the $n\times n$…

Computer Science and Game Theory · Computer Science 2025-10-16 Andrea Collevecchio , Gabor Lugosi , Adrian Vetta , Rui-Ray Zhang