Methods for Solving Generalized Nash Equilibrium | Zendy

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Methods for Solving Generalized Nash Equilibrium

Author(s) -

Biao Qu,

Jing Zhao

Publication year - 2013

Publication title -

journal of applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.307

H-Index - 43

eISSN - 1687-0042

pISSN - 1110-757X

DOI - 10.1155/2013/762165

Subject(s) - nash equilibrium , extension (predicate logic) , mathematical optimization , convergence (economics) , epsilon equilibrium , best response , mathematics , mathematical economics , descent (aeronautics) , correlated equilibrium , stationary point , computer science , game theory , equilibrium selection , economics , repeated game , mathematical analysis , aerospace engineering , engineering , programming language , economic growth

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. © 2013 Biao Qu and Jing Zhao.

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