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A second-order cone programming formulation for two player zero-sum games with chance constraints

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  • Singh, Vikas Vikram
  • Lisser, Abdel

Abstract

We consider a two player finite strategic zero-sum game where each player has stochastic linear constraints. We formulate the stochastic constraints of each player as chance constraints. We show the existence of a saddle point equilibrium in mixed strategies if the row vectors of the random matrices defining the stochastic constraints are elliptically symmetric distributed random vectors. We further show that a saddle point equilibrium can be obtained from the optimal solutions of a primal-dual pair of second-order cone programs.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:275:y:2019:i:3:p:839-845
    DOI: 10.1016/j.ejor.2019.01.010
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    References listed on IDEAS

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    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.
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    3. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, September.
    4. 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.
    5. Roger A. Blau, 1974. "Random-Payoff Two-Person Zero-Sum Games," Operations Research, INFORMS, vol. 22(6), pages 1243-1251, December.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. 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.
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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. 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.
    3. 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).
    4. Ming Liu & Rongfan Liu & E Zhang & Chengbin Chu, 2022. "Eco-friendly container transshipment route scheduling problem with repacking operations," Journal of Combinatorial Optimization, Springer, vol. 43(5), pages 1010-1035, July.
    5. Ming Liu & Rongfan Liu & E Zhang & Chengbin Chu, 0. "Eco-friendly container transshipment route scheduling problem with repacking operations," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-26.

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