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Characterization of a value for games under restricted cooperation

Author

Listed:
  • M. Josune Albizuri

    (Basque Country University (UPV/EHU))

  • Satoshi Masuya

    (Daito Bunka University)

  • José M. Zarzuelo

    (Basque Country University (UPV/EHU))

Abstract

The object of this paper is to study restricted cooperative games, that is, cooperative games for which the worth of some coalitions is unknown. We consider a value for these restricted cooperative games whose definition is based on the Harsanyi’s dividends approach, and can therefore be seen as an extension of the Shapley value. We provide a characterization of this value with three axioms: Carrier, Symmetric-partnership and Additivity, which are similar to those proposed by Shapley (in: Kuhn and Tucker (eds) Contributions to the theory of games, Princeton University Press, Princeton, 1953). In addition, we characterize this value on the subclass of restricted cooperative simple games. Finally, we apply this value for restricted cooperative games to analyze the power distribution of the Catalonian Parliament in 1980 and compare the results with those of the coalitional value in Carreras and Owen (Math Soc Sci 15:87–92, 1988).

Suggested Citation

  • M. Josune Albizuri & Satoshi Masuya & José M. Zarzuelo, 2022. "Characterization of a value for games under restricted cooperation," Annals of Operations Research, Springer, vol. 318(2), pages 773-785, November.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:2:d:10.1007_s10479-022-04768-3
    DOI: 10.1007/s10479-022-04768-3
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    References listed on IDEAS

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    Cited by:

    1. 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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