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The Shapley Value for Stochastic Cooperative Game

Author

Listed:
  • Ying Ma
  • Zuofeng Gao
  • Wei Li
  • Ning Jiang
  • Lei Guo

Abstract

In this paper we extend the notion of Shapley value to the stochastic cooperative games. We give the definition of marginal vector to the stochastic cooperative games and we define the Shapley value for this game. Furthermore, we discuss the axioms of the Shapley value and give the proofs of these axioms.

Suggested Citation

  • Ying Ma & Zuofeng Gao & Wei Li & Ning Jiang & Lei Guo, 2008. "The Shapley Value for Stochastic Cooperative Game," Modern Applied Science, Canadian Center of Science and Education, vol. 2(4), pages 1-76, July.
    • Handle: RePEc:ibn:masjnl:v:2:y:2008:i:4:p:76
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    References listed on IDEAS

    as
    1. Suijs, Jeroen & Borm, Peter & De Waegenaere, Anja & Tijs, Stef, 1999. "Cooperative games with stochastic payoffs," European Journal of Operational Research, Elsevier, vol. 113(1), pages 193-205, February.
    2. Khmelnitskaya, Anna B., 1999. "Marginalist and efficient values for TU games," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 45-54, July.
    3. Hamers, Herbert & Suijs, Jeroen & Tijs, Stef & Borm, Peter, 1996. "The Split Core for Sequencing Games," Games and Economic Behavior, Elsevier, vol. 15(2), pages 165-176, August.
    4. Suijs, Jeroen & Borm, Peter, 1999. "Stochastic Cooperative Games: Superadditivity, Convexity, and Certainty Equivalents," Games and Economic Behavior, Elsevier, vol. 27(2), pages 331-345, May.
    5. Bilbao, J. M., 1998. "Axioms for the Shapley value on convex geometries," European Journal of Operational Research, Elsevier, vol. 110(2), pages 368-376, October.
    6. Rothschild, R., 2001. "On the use of a modified Shapley value to determine the optimal size of a cartel," Journal of Economic Behavior & Organization, Elsevier, vol. 45(1), pages 37-47, May.
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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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