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A globalized Newton method for the computation of normalized Nash equilibria

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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.

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Authors and Affiliations

  1. Institute of Mathematics, University of Würzburg, Emil-Fischer-Str., 97074, Würzburg, Germany

    Axel Dreves, Anna von Heusinger & Christian Kanzow

  2. Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan

    Masao Fukushima

Authors
  1. Axel Dreves
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  2. Anna von Heusinger
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  3. Christian Kanzow
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  4. Masao Fukushima
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Correspondence to Masao Fukushima.

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Dreves, A., von Heusinger, A., Kanzow, C. et al. A globalized Newton method for the computation of normalized Nash equilibria. J Glob Optim 56, 327–340 (2013). https://doi.org/10.1007/s10898-011-9824-9

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  • DOI: https://doi.org/10.1007/s10898-011-9824-9

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