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Random Games Under Elliptically Distributed Dependent Joint Chance Constraints

Author

Listed:
  • Hoang Nam Nguyen

    (Université Paris Saclay, CNRS, CentraleSupelec)

  • Abdel Lisser

    (Université Paris Saclay, CNRS, CentraleSupelec)

  • Vikas Vikram Singh

    (Indian Institute of Technology Delhi)

Abstract

We study an n-player game with random payoffs and continuous strategy sets. The payoff function of each player is defined by its expected value and the strategy set of each player is defined by a joint chance constraint. The random constraint vectors defining the joint chance constraint are dependent and follow elliptically symmetric distributions. The Archimedean copula is used to capture the dependence among random constraint vectors. We propose a reformulation of the joint chance constraint of each player. Under mild assumptions on the players’ payoff functions and 1-dimensional spherical distribution functions, we show that there exists a Nash equilibrium of the game.

Suggested Citation

  • Hoang Nam Nguyen & Abdel Lisser & Vikas Vikram Singh, 2022. "Random Games Under Elliptically Distributed Dependent Joint Chance Constraints," Journal of Optimization Theory and Applications, Springer, vol. 195(1), pages 249-264, October.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:1:d:10.1007_s10957-022-02077-0
    DOI: 10.1007/s10957-022-02077-0
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    References listed on IDEAS

    as
    1. Cheng, Jianqiang & Leung, Janny & Lisser, Abdel, 2016. "Random-payoff two-person zero-sum game with joint chance constraints," European Journal of Operational Research, Elsevier, vol. 252(1), pages 213-219.
    2. Ran Ji & Miguel A. Lejeune, 2018. "Risk-budgeting multi-portfolio optimization with portfolio and marginal risk constraints," Annals of Operations Research, Springer, vol. 262(2), pages 547-578, March.
    3. Vikas Vikram Singh & Abdel Lisser, 2018. "A Characterization of Nash Equilibrium for the Games with Random Payoffs," Journal of Optimization Theory and Applications, Springer, vol. 178(3), pages 998-1013, September.
    4. Singh, Vikas Vikram & Lisser, Abdel & Arora, Monika, 2021. "An equivalent mathematical program for games with random constraints," Statistics & Probability Letters, Elsevier, vol. 174(C).
    5. Singh, Vikas Vikram & Lisser, Abdel, 2019. "A second-order cone programming formulation for two player zero-sum games with chance constraints," European Journal of Operational Research, Elsevier, vol. 275(3), pages 839-845.
    6. René Henrion & Cyrille Strugarek, 2011. "Convexity of Chance Constraints with Dependent Random Variables: The Use of Copulae," International Series in Operations Research & Management Science, in: Marida Bertocchi & Giorgio Consigli & Michael A. H. Dempster (ed.), Stochastic Optimization Methods in Finance and Energy, edition 1, chapter 0, pages 427-439, Springer.
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    Cited by:

    1. Filippo Fabiani & Barbara Franci, 2023. "On Distributionally Robust Generalized Nash Games Defined over the Wasserstein Ball," Journal of Optimization Theory and Applications, Springer, vol. 199(1), pages 298-309, October.
    2. Nguyen, Hoang Nam & Lisser, Abdel & Singh, Vikas Vikram, 2024. "Random games under normal mean–variance mixture distributed independent linear joint chance constraints," Statistics & Probability Letters, Elsevier, vol. 208(C).
    3. Rossana Riccardi & Giorgia Oggioni & Elisabetta Allevi & Abdel Lisser, 2023. "Complementarity formulation of games with random payoffs," Computational Management Science, Springer, vol. 20(1), pages 1-32, December.

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