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Random games under normal mean–variance mixture distributed independent linear joint chance constraints

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  • Nguyen, Hoang Nam
  • Lisser, Abdel
  • Singh, Vikas Vikram

Abstract

In this paper, we study an n player game where the payoffs as well as the strategy sets are defined using random variables. The payoff function of each player is defined using expected value function and his/her strategy set is defined using a linear joint chance constraint. The random constraint vectors defining the joint chance constraint are independent and follow normal mean–variance mixture distributions. For each player, we reformulate the joint chance constraint in order to prove the existence of a Nash equilibrium using the Kakutani fixed-point theorem under mild assumptions. We illustrate our theoretical results by considering a game between two competing firms in financial market.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s0167715224000051
    DOI: 10.1016/j.spl.2024.110036
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Naderi, Mehrdad & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2023. "Robust mixture regression modeling based on the normal mean-variance mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    4. Lampariello, Lorenzo & Neumann, Christoph & Ricci, Jacopo M. & Sagratella, Simone & Stein, Oliver, 2021. "Equilibrium selection for multi-portfolio optimization," European Journal of Operational Research, Elsevier, vol. 295(1), pages 363-373.
    5. Singh, Vikas Vikram & Lisser, Abdel & Arora, Monika, 2021. "An equivalent mathematical program for games with random constraints," Statistics & Probability Letters, Elsevier, vol. 174(C).
    6. 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.
    7. Shen Peng & Navnit Yadav & Abdel Lisser & Vikas Vikram Singh, 2021. "Chance-constrained games with mixture distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 94(1), pages 71-97, August.
    8. 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.
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