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Journal of Applied Mathematics
Volume 2013, Article ID 762165, 6 pages
Research Article

Methods for Solving Generalized Nash Equilibrium

School of Management, Qufu Normal University, Rizhao, Shandong 276826, China

Received 12 October 2012; Revised 5 January 2013; Accepted 17 January 2013

Academic Editor: Ya Ping Fang

Copyright © 2013 Biao Qu and Jing Zhao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.