A smoothing method for a class of generalized Nash equilibrium problems

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• 作者：Jun-Feng Lai (1)
  Jian Hou (2)
  Zong-Chuan Wen (2)
  
  1. Science College ; Inner Mongolia University of Technology ; Hohhot ; 010051 ; China
  2. Management College ; Inner Mongolia University of Technology ; Hohhot ; 010051 ; China
  
• 关键词：standard Nash equilibrium problem ; generalized Nash equilibrium problem ; normalized Nash equilibrium ; Nikaido ; Isoda function ; M ; stationary point
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,290 KB
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• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

The generalized Nash equilibrium problem is an extension of the standard Nash equilibrium problem where both the utility function and the strategy space of each player depend on the strategies chosen by all other players. Recently, the generalized Nash equilibrium problem has emerged as an effective and powerful tool for modeling a wide class of problems arising in many fields and yet solution algorithms are extremely scarce. In this paper, using a regularized Nikaido-Isoda function, we reformulate the generalized Nash equilibrium problem as a mathematical program with complementarity constraints (MPCC). We then propose a suitable method for this MPCC and under some conditions, we establish the convergence of the proposed method by showing that any accumulation point of the generated sequence is a M-stationary point of the MPCC. Numerical results on some generalized Nash equilibrium problems are reported to illustrate the behavior of our approach.