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Solution of a Satisficing Model for Random Payoff Games

Author

Listed:
  • R. G. Cassidy

    (Carnegie-Mellon University)

  • C. A. Field

    (Dalhousie University)

  • M. J. L. Kirby

    (Dalhousie University)

Abstract

In this paper, we consider a "satisficing" criterion to solve two-person zero-sum games with random payoffs. In particular, a player wants to maximize the payoff level he can achieve with a specified confidence. The problem reduces to solving a nonconvex mathematical programming problem. The main result shows that solving this problem is equivalent to finding the root of an equation whose values are determined by solving a linear problem. This linear problem results from maximizing the confidence with fixed payoff level.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:19:y:1972:i:3:p:266-271
    DOI: 10.1287/mnsc.19.3.266
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    Citations

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    Cited by:

    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. James J. Buckley, 1983. "Decision Making Under Risk: A Comparison of Bayesian and Fuzzy Set Methods," Risk Analysis, John Wiley & Sons, vol. 3(3), pages 157-168, September.
    3. Singh, Vikas Vikram & Lisser, Abdel & Arora, Monika, 2021. "An equivalent mathematical program for games with random constraints," Statistics & Probability Letters, Elsevier, vol. 174(C).
    4. Chunsheng Cui & Zhongwei Feng & Chunqiao Tan, 2018. "Credibilistic Loss Aversion Nash Equilibrium for Bimatrix Games with Triangular Fuzzy Payoffs," Complexity, Hindawi, vol. 2018, pages 1-16, December.
    5. Xiangfeng Yang & Jinwu Gao, 2017. "Bayesian equilibria for uncertain bimatrix game with asymmetric information," Journal of Intelligent Manufacturing, Springer, vol. 28(3), pages 515-525, March.
    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. Longsheng Sun & Mark H. Karwan & Changhyun Kwon, 2018. "Generalized Bounded Rationality and Robust Multicommodity Network Design," Operations Research, INFORMS, vol. 66(1), pages 42-57, 1-2.
    8. 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.
    9. 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.

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