A globalized Newton method for the computation of normalized Nash equilibria

Authors:
Axel Dreves;Anna Heusinger;Christian Kanzow;Masao Fukushima
Affiliations:
Institute of Mathematics, University of Würzburg, Würzburg, Germany 97074;Institute of Mathematics, University of Würzburg, Würzburg, Germany 97074;Institute of Mathematics, University of Würzburg, Würzburg, Germany 97074;Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, Japan 606-8501
Venue:
Journal of Global Optimization
Year:
2013

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Abstract

The generalized Nash equilibrium is a Nash game, where not only the players' cost functions, but also the constraints of a player depend on the rival players decisions. We present a globally convergent algorithm that is suited for the computation of a normalized Nash equilibrium in the generalized Nash game with jointly convex constraints. The main tool is the regularized Nikaido---Isoda function as a basis for a locally convergent nonsmooth Newton method and, in another way, for the definition of a merit function for globalization. We conclude with some numerical results.