Non-cooperative games with minmax objectives
type: Item
instance of: scholarly article
title: Non-cooperative games with minmax objectives
zbMATH Open document ID: 1307.91013
author: Francisco Facchinei
author: Jong-Shi Pang
author: Gesualdo Scutari
published in: Computational Optimization and Applications
publication date: 2014-09-18T00:00:00Z
review text: The authors consider noncooperative games where each player's penalty function is composite, with the second term being a common nonsmooth function, which is supposed to be given by a max-type one. They propose two ways to treat this problem. Firstly, they replace it with the enlarged one, where the common term is transferred to an additional player with the corresponding smooth payoff function, thus removing the maximum operation. Secondly, they suggest a smoothing approximation of the common term, which gives a parametric family of Nash equilibrium problems. Convergence results for the general best response algorithm are given. Its diagonalized versions are also discussed.
Mathematics Subject Classification ID: 91A10
Mathematics Subject Classification ID: 90C47
Mathematics Subject Classification ID: 90C31
zbMATH DE Number: 6345667
zbMATH Keywords: noncooperative games
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: composite penalty
zbMATH Keywords: smooth approximation
zbMATH Keywords: best response
zbMATH Keywords: diagonalization
reviewed by: Igor V. Konnov
MaRDI profile type: Publication
full work available at URL: s10589-014-9642-3
OpenAlex ID: W1982698550
cites work: Iterative approximation of fixed points
cites work: Q4001523
cites work: Gradient consistency for integral-convolution smoothing functions
cites work: Semiconcave functions, Hamilton-Jacobi equations, and optimal control
cites work: Smoothing methods for nonsmooth, nonconvex minimization
cites work: On the solution of the KKT conditions of generalized Nash equilibrium problems
cites work: Polymatrix Games with Joint Constraints
cites work: The Minimization of Semicontinuous Functions: Mollifier Subgradients
cites work: Generalized Nash equilibrium problems
cites work: Penalty Methods for the Solution of Generalized Nash Equilibrium Problems
cites work: Finite-Dimensional Variational Inequalities and Complementarity Problems
cites work: Q3079678
cites work: VI-constrained hemivariational inequalities: distributed algorithms and power control in ad-hoc networks
cites work: Decomposition algorithms for generalized potential games
cites work: Restricted generalized Nash equilibria and controlled penalty algorithm
cites work: Approximations of Nash equilibria
cites work: Newton's method for computing a normalized equilibrium in the generalized Nash game through fixed point formulation
cites work: Differential Topology
cites work: Variational convergence of bivariate functions: Lopsided convergence
cites work: Addressing supply-side risk in uncertain power markets: stochastic Nash models, scalable algorithms and error analysis
cites work: Numerical solutions to coupled-constraint (or generalised Nash) equilibrium problems
cites work: Gap function approach to the generalized Nash equilibrium problem
cites work: On the variational equilibrium as a refinement of the generalized Nash equilibrium
cites work: Revisiting generalized Nash games and variational inequalities
cites work: Decentralized Resource Allocation in Dynamic Networks of Agents
cites work: Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints
cites work: Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games
cites work: Nonconvex Games with Side Constraints
cites work: Q3028166
cites work: Variational Analysis
cites work: Existence and Uniqueness of Equilibrium Points for Concave N-Person Games
cites work: Real and Complex Monotone Communication Games
cites work: Decomposition by Partial Linearization: Parallel Optimization of Multi-Agent Systems
cites work: On relaxation algorithms in computation of noncooperative equilibria
cites work: Strong and Weak Convexity of Sets and Functions
cites work: On stochastic gradient and subgradient methods with adaptive steplength sequences
DOI: 10.1007/S10589-014-9642-3
description: scientific article; zbMATH DE number 6345667