Methods for Solving Generalized Nash Equilibrium. (14th February 2013)

• Record Type: Journal Article
• Authors: Qu, Biao; Zhao, Jing
• Other Names: Fang Ya Ping Academic Editor.
• Is Part Of: Journal of applied mathematics. Volume 2013(2013)
• Publication Date: 2013-02-14
• Subjects: Mathematics -- Periodicals; 519.05
• DOI: 10.1155/2013/762165
• Languages: English
• ISSNs: 1110-757X

Abstract

Abstract : The generalized Nash equilibrium problem (GNEP) is an extension of the standard Nash equilibrium problem (NEP), in which each player's strategy set may depend on the rival player's strategies. In this paper, we present two descent type methods. The algorithms are based on a reformulation of the generalized Nash equilibrium using Nikaido-Isoda function as unconstrained optimization. We prove that our algorithms are globally convergent and the convergence analysis is not based on conditions guaranteeing that every stationary point of the optimization problem is a solution of the GNEP.