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Linear and symmetric allocation methods for partially defined cooperative games

Author

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  • David Housman

    (Department of Mathematics, Goshen College, 1700 South Main Street, Goshen, IN 46526, USA)

Abstract

A partially defined cooperative game is a coalition function form game in which some of the coalitional worths are not known. An application would be cost allocation of a joint project among so many players that the determination of all coalitional worths is prohibitive. This paper generalizes the concept of the Shapley value for cooperative games to the class of partially defined cooperative games. Several allocation method characterization theorems are given utilizing linearity, symmetry, formulation independence, subsidy freedom, and monotonicity properties. Whether a value exists or is unique depends crucially on the class of games under consideration.

Suggested Citation

  • David Housman, 2002. "Linear and symmetric allocation methods for partially defined cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 377-404.
    • Handle: RePEc:spr:jogath:v:30:y:2002:i:3:p:377-404
    Note: Received June 1996/Revised August 2001
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    References listed on IDEAS

    as
    1. Curiel, I. & Potters, J.A.M. & Rajendra Prasad, V. & Tijs, S.H. & Veltman, B., 1993. "Cooperation in one machine scheduling," Other publications TiSEM 9c5ceec5-2080-4b5c-98d5-0, Tilburg University, School of Economics and Management.
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    4. Pradeep Dubey & Abraham Neyman & Robert J. Weber, 1979. "Value Theory without Efficiency," Cowles Foundation Discussion Papers 513, Cowles Foundation for Research in Economics, Yale University.
    5. Monderer, Dov, 1988. "Values and Semivalues on Subspaces of Finite Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 17(4), pages 301-310.
    6. Willson, Stephen J, 1993. "A Value for Partially Defined Cooperative Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 371-384.
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    Cited by:

    1. Satoshi Masuya & Masahiro Inuiguchi, 2016. "A fundamental study for partially defined cooperative games," Fuzzy Optimization and Decision Making, Springer, vol. 15(3), pages 281-306, September.
    2. Tobias Hiller, 2013. "The distribution of power in governing coalitions of the German Laender," Applied Economics Letters, Taylor & Francis Journals, vol. 20(12), pages 1155-1159, August.
    3. Satoshi Masuya, 2023. "Two Approaches to Estimate the Shapley Value for Convex Partially Defined Games," Mathematics, MDPI, vol. 12(1), pages 1-15, December.

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