Parametrized variational inequality approaches to generalized Nash equilibrium problems with shared constraints

  • Authors:

  • Koichi Nabetani;Paul Tseng;Masao Fukushima

  • Affiliations:

  • Research and Development Headquarters NTT DATA CORPORATION, Tokyo, Japan;Department of Mathematics, University of Washington, Seattle, USA 98195;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501

  • Venue:
  • Computational Optimization and Applications
  • Year:
  • 2011

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Abstract

We consider the generalized Nash equilibrium problem (GNEP), in which each player's strategy set may depend on the rivals' strategies through shared constraints. A practical approach to solving this problem that has received increasing attention lately entails solving a related variational inequality (VI). From the viewpoint of game theory, it is important to find as many GNEs as possible, if not all of them. We propose two types of parametrized VIs related to the GNEP, one price-directed and the other resource-directed. We show that these parametrized VIs inherit the monotonicity properties of the original VI and, under mild constraint qualifications, their solutions yield all GNEs. We propose strategies to sample in the parameter spaces and show, through numerical experiments on benchmark examples, that the GNEs found by the parametrized VI approaches are widely distributed over the GNE set.