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An equivalent mathematical program for games with random constraints

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  • Singh, Vikas Vikram
  • Lisser, Abdel
  • Arora, Monika

Abstract

We consider an n-player chance-constrained game under elliptically symmetric distributions. For a confidence level greater than 0.5 and certain class of payoff functions and strategy sets, we suitably construct an equivalent mathematical program whose global maximizer is a Nash equilibrium.

Suggested Citation

  • Singh, Vikas Vikram & Lisser, Abdel & Arora, Monika, 2021. "An equivalent mathematical program for games with random constraints," Statistics & Probability Letters, Elsevier, vol. 174(C).
    • Handle: RePEc:eee:stapro:v:174:y:2021:i:c:s0167715221000547
    DOI: 10.1016/j.spl.2021.109092
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    References listed on IDEAS

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    1. Gilli, Manfred & Maringer, Dietmar & Schumann, Enrico, 2011. "Numerical Methods and Optimization in Finance," Elsevier Monographs, Elsevier, edition 1, number 9780123756626.
    2. 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.
    3. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, November.
    4. R. G. Cassidy & C. A. Field & M. J. L. Kirby, 1972. "Solution of a Satisficing Model for Random Payoff Games," Management Science, INFORMS, vol. 19(3), pages 266-271, November.
    5. Jianjian Wang & Feng He & Xin Shi, 2019. "Numerical solution of a general interval quadratic programming model for portfolio selection," PLOS ONE, Public Library of Science, vol. 14(3), pages 1-16, March.
    6. 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.
    7. 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.
    8. Roger A. Blau, 1974. "Random-Payoff Two-Person Zero-Sum Games," Operations Research, INFORMS, vol. 22(6), pages 1243-1251, December.
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    Cited by:

    1. 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).
    2. 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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