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Distributionally robust chance-constrained games: existence and characterization of Nash equilibrium

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Abstract

We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider two types of distributional uncertainty sets. We show the existence of a mixed strategy Nash equilibrium of a distributionally robust chance-constrained game corresponding to both types of distributional uncertainty sets. For each case, we show a one-to-one correspondence between a Nash equilibrium of a game and a global maximum of a certain mathematical program.

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Acknowledgments

This research was supported by Fondation DIGITEO, SUN Grant No. 2014-0822D.

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Authors and Affiliations

  1. Laboratoire de Recherche en Informatique, Université Paris Sud XI, Bât 650, 91405, Orsay Cedex, France

    Vikas Vikram Singh & Abdel Lisser

  2. Laboratoire Génie Industriel, CentraleSupélec, Université Paris-Saclay, Grande Voie des Vignes, 92 290, Châtenay-Malabry, France

    Oualid Jouini

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  1. Vikas Vikram Singh
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  2. Oualid Jouini
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  3. Abdel Lisser
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Correspondence to Vikas Vikram Singh.

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Singh, V.V., Jouini, O. & Lisser, A. Distributionally robust chance-constrained games: existence and characterization of Nash equilibrium. Optim Lett 11, 1385–1405 (2017). https://doi.org/10.1007/s11590-016-1077-6

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  • DOI: https://doi.org/10.1007/s11590-016-1077-6

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