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Related papers: Rational Generalized Nash Equilibrium Problems

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In this paper, we propose an equilibrium-seeking algorithm for finding generalized Nash equilibria of non-cooperative monotone convex quadratic games. Specifically, we recast the Nash equilibrium-seeking problem as variational inequality…

Optimization and Control · Mathematics 2024-03-21 Bingqi Liu , Dominic Liao-McPherson

We investigate a modular convex Nash equilibrium problem involving nonsmooth functions acting on linear mixtures of strategies, as well as smooth coupling functions. An asynchronous block-iterative decomposition method is proposed to solve…

Optimization and Control · Mathematics 2021-11-03 Minh N. Bùi , Patrick L. Combettes

This paper studies generalized semi-infinite programs (GSIPs) given by polynomials. We propose a hierarchy of polynomial optimization relaxations to solve them. They are based on Lagrange multiplier expressions and polynomial extensions.…

Optimization and Control · Mathematics 2025-04-15 Xiaomeng Hu , Jiawang Nie

The symmetric generalized eigenvalue problem (SGEP) is a fundamental concept in numerical linear algebra. It captures the solution of many classical machine learning problems such as canonical correlation analysis, independent components…

Machine Learning · Computer Science 2023-04-26 Ian Gemp , Charlie Chen , Brian McWilliams

In this work, we study the distributed Nash equilibrium seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A distributed regularized penalty method is proposed. The…

Optimization and Control · Mathematics 2021-09-28 Chao Sun , Guoqiang Hu

We consider generalized Nash equilibrium (GNE) problems in games with strongly monotone pseudo-gradients and jointly linear coupling constraints. We establish the convergence rate of a payoff-based approach intended to learn a variational…

Optimization and Control · Mathematics 2024-11-14 Tatiana Tatarenko , Maryam Kamgarpour

This paper presents an exact penalization theory of the generalized Nash equilibrium problem (GNEP) that has its origin from the renowned Arrow-Debreu general economic equilibrium model. While the latter model is the foundation of much of…

Computer Science and Game Theory · Computer Science 2018-12-04 Qin Ba , Jong-Shi Pang

We introduce an extended mathematical programming framework for specifying equilibrium problems and their variational representations, such as generalized Nash equilibrium, multiple optimization problems with equilibrium constraints, and…

Optimization and Control · Mathematics 2018-06-07 Youngdae Kim , Michael C. Ferris

Nash equilibrium is the most commonly-used notion of equilibrium in game theory. However, it suffers from numerous problems. Some are well known in the game theory community; for example, the Nash equilibrium of repeated prisoner's dilemma…

Computer Science and Game Theory · Computer Science 2008-12-18 Joseph Y. Halpern

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

With the proliferation of distributed generators and energy storage systems, traditional passive consumers in power systems have been gradually evolving into the so-called "prosumers", i.e., proactive consumers, which can both produce and…

Systems and Control · Electrical Eng. & Systems 2020-04-10 Zhaojian Wang , Feng Liu , Zhiyuan Ma , Yue Chen , Mengshuo Jia , Wei Wei , Qiuwei Wu

We address the generalized Nash equilibrium seeking problem in a partial-decision information scenario, where each agent can only exchange information with some neighbors, although its cost function possibly depends on the strategies of all…

Optimization and Control · Mathematics 2021-12-14 Mattia Bianchi , Giuseppe Belgioioso , Sergio Grammatico

We deal with the generalized Nash game proposed by Rosen, which is a game with strategy sets that are coupled across players through a shared constraint. A reduction to a classical game is shown, and as a consequence, Rosen's result can be…

Optimization and Control · Mathematics 2023-07-10 Carlos Calderón , John Cotrina

Nash equilibrium} (NE) can be stated as a formal theorem on a multilinear form, free of game theory terminology. On the other hand, inspired by this formalism, we state and prove a {\it multilinear minimax theorem}, a generalization of von…

Computer Science and Game Theory · Computer Science 2024-01-01 Bahman Kalantari

For generalized Nash equilibrium problems (GNEP) with shared constraints we focus on the notion of normalized Nash equilibrium in the nonconvex setting. The property of nondegeneracy for normalized Nash equilibria is introduced.…

Optimization and Control · Mathematics 2022-05-30 Vladimir Shikhman

We consider distributed computation of generalized Nash equilibrium (GNE) over networks, in games with shared coupling constraints. Existing methods require that each player has full access to opponents' decisions. In this paper, we assume…

Optimization and Control · Mathematics 2024-10-30 Lacra Pavel

We introduce the use of generative adversarial learning to compute equilibria in general game-theoretic settings, specifically the generalized Nash equilibrium (GNE) in pseudo-games, and its specific instantiation as the competitive…

Computer Science and Game Theory · Computer Science 2023-02-21 Denizalp Goktas , David C. Parkes , Ian Gemp , Luke Marris , Georgios Piliouras , Romuald Elie , Guy Lever , Andrea Tacchetti

In this paper we study the existence and uniqueness of Nash equilibria (solution to competition-wise problems, with several controls trying to reach possibly different goals) associated to linear partial differential equations and show…

Optimization and Control · Mathematics 2019-09-02 Angel Manuel Ramos

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

Optimization and Control · Mathematics 2025-07-18 Tatiana Tatarenko , Angelia Nedich

This work examines a stochastic formulation of the generalized Nash equilibrium problem (GNEP) where agents are subject to randomness in the environment of unknown statistical distribution. We focus on fully-distributed online learning by…

Computer Science and Game Theory · Computer Science 2017-06-28 Chung-Kai Yu , Mihaela van der Schaar , Ali H. Sayed