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Coalitional and Chance-Constrained Solutions to n -Person Games, II: Two-Stage Solutions

Author

Listed:
  • A. Charnes

    (University of Texas, Austin, Texas)

  • Daniel Granot

    (Simon Frazer University, Burnaby, British Columbia)

Abstract

We extend the theory of n -person cooperative games in characteristic function form to games with stochastic characteristic functions. We propose a payoff process to the players in these games that is composed of two parts. In the first part the players are promised some prior payoffs. In the second part we use the two-stage solution concepts to modify the prior payoffs in a manner acceptable to the players. We verify the existence of these solution concepts and explore some of their properties.

Suggested Citation

  • A. Charnes & Daniel Granot, 1977. "Coalitional and Chance-Constrained Solutions to n -Person Games, II: Two-Stage Solutions," Operations Research, INFORMS, vol. 25(6), pages 1013-1019, December.
    • Handle: RePEc:inm:oropre:v:25:y:1977:i:6:p:1013-1019
    DOI: 10.1287/opre.25.6.1013
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    Cited by:

    1. Suijs, J.P.M. & Borm, P.E.M., 1996. "Cooperative Games with Stochastic Payoffs : Determanistic Equivalents," Research Memorandum 713, Tilburg University, School of Economics and Management.
    2. Donald Nganmegni Njoya & Issofa Moyouwou & Nicolas Gabriel Andjiga, 2021. "The equal-surplus Shapley value for chance-constrained games on finite sample spaces," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 93(3), pages 463-499, June.
    3. Ichiro Nishizaki & Tomohiro Hayashida & Shinya Sekizaki & Kojiro Furumi, 2023. "A two-stage linear production planning model with partial cooperation under stochastic demands," Annals of Operations Research, Springer, vol. 320(1), pages 293-324, January.
    4. Yang, Jian & Li, Jianbin, 2020. "Cooperative game with nondeterministic returns," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 123-140.
    5. Kholodkova, Victoria Vladimirovna, 2017. "Cooperative games in the economic and political world relations," Economic Consultant, Roman I. Ostapenko, vol. 20(4), pages 24-29.
    6. Pavel Konyukhovskiy & Victoria Holodkova & Aleksander Titov, 2019. "Modeling Competition between Countries in the Development of Arctic Resources," Resources, MDPI, vol. 8(1), pages 1-17, March.
    7. Kim, Jeong-Yoo & Lee, Seewoo, 2019. "Apportionment of liability by the stochastic Shapley value," International Review of Law and Economics, Elsevier, vol. 60(C).

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