Year: 2012
Author: Jian Hou, Junfeng Lai
Communications in Mathematical Research , Vol. 28 (2012), Iss. 2 : pp. 181–192
Abstract
The generalized Nash equilibrium problem (GNEP) is a generalization of the standard Nash equilibrium problem (NEP), in which both the utility function and the strategy space of each player depend on the strategies chosen by all other players. This problem has been used to model various problems in applications. However, the convergent solution algorithms are extremely scare in the literature. In this paper, we present an incremental penalty method for the GNEP, and show that a solution of the GNEP can be found by solving a sequence of smooth NEPs. We then apply the semismooth Newton method with Armijo line search to solve latter problems and provide some results of numerical experiments to illustrate the proposed approach.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2012-CMR-19058
Communications in Mathematical Research , Vol. 28 (2012), Iss. 2 : pp. 181–192
Published online: 2012-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Nash equilibrium problem generalized Nash equilibrium problem logarithmic barrier function quasi-variational inequality semismooth Newton method.