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Games with distributionally robust joint chance constraints

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Abstract

This paper studies an n-player non-cooperative game where each player has expected-value payoff function and chance-constrained strategy set. We consider the case where the row vectors defining the constraints are independent random vectors whose probability distributions are not completely known and belong to a certain distributional uncertainty set. The chance-constrained strategy sets are defined using a distributionally robust framework. We consider one density based uncertainty set and four two-moments based uncertainty sets. One of the considered uncertainty sets is based on a nonnegative support. Under the standard assumptions on the players’ payoff functions, we show that there exists a Nash equilibrium of a distributionally robust chance-constrained game for each uncertainty set. As an application, we study Cournot competition in electricity market and perform the numerical experiments for the case of two electricity firms.

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Acknowledgements

This research was supported by DST/CEFIPRA Project No. IFC/4117/DST-CNRS-5th call/2017-18/2 and CNRS Project No. AR/SB:2018-07-440.

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Authors and Affiliations

  1. Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden

    Shen Peng

  2. Laboratory of Signals and Systems, CentraleSupelec, Bat Breguet, 3 Rue Joliot Curie, 91190, Gif-sur-Yvette, France

    Abdel Lisser

  3. Department of Mathematics, IIT Delhi, New Delhi, India

    Vikas Vikram Singh, Nalin Gupta & Eshan Balachandar

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  1. Shen Peng
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  2. Abdel Lisser
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  3. Vikas Vikram Singh
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  5. Eshan Balachandar
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Correspondence to Vikas Vikram Singh.

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Peng, S., Lisser, A., Singh, V.V. et al. Games with distributionally robust joint chance constraints. Optim Lett 15, 1931–1953 (2021). https://doi.org/10.1007/s11590-021-01700-9

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