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Characterizations of a multi-choice value


  • José Zarzuelo

    (Department of Applied Mathematics, University of Pai´s Vasco, E-48015 Bilbao, Spain)

  • Marco Slikker

    () (Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)

  • Flip Klijn

    () (Department of Econometrics and CentER, Tilburg University, P.O. Box 90153, 5000 LE Tilburg, The Netherlands)


A multi-choice game is a generalization of a cooperative game in which each player has several activity levels. We study the extended Shapley value as proposed by Derks and Peters (1993). Van den Nouweland (1993) provided a characterization that is an extension of Young's (1985) characterization of the Shapley value. Here we provide several other characterizations, one of which is the analogue of Shapley's (1953) original characterization. The three other characterizations are inspired by Myerson's (1980) characterization of the Shapley value using balanced contributions.

Suggested Citation

  • José Zarzuelo & Marco Slikker & Flip Klijn, 1999. "Characterizations of a multi-choice value," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(4), pages 521-532.
  • Handle: RePEc:spr:jogath:v:28:y:1999:i:4:p:521-532
    Note: Received: November 1997/final version: February 1999

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    References listed on IDEAS

    1. Derks, Jean & Peters, Hans, 1993. "A Shapley Value for Games with Restricted Coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 351-360.
    2. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
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    Cited by:

    1. S. Béal & A. Lardon & E. Rémila & P. Solal, 2012. "The average tree solution for multi-choice forest games," Annals of Operations Research, Springer, vol. 196(1), pages 27-51, July.
    2. Fanyong Meng & Qiang Zhang & Xiaohong Chen, 2017. "Fuzzy Multichoice Games with Fuzzy Characteristic Functions," Group Decision and Negotiation, Springer, vol. 26(3), pages 565-595, May.
    3. Mustapha Ridaoui & Michel Grabisch & Christophe Labreuche, 2017. "Axiomatization of an importance index for Generalized Additive Independence models," Documents de travail du Centre d'Economie de la Sorbonne 17048, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    4. Michel Grabisch & Christophe Labreuche & Mustapha Ridaoui, 2018. "On importance indices in multicriteria decision making," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01815012, HAL.
    5. repec:spr:compst:v:73:y:2011:i:1:p:55-73 is not listed on IDEAS
    6. Hwang, Yan-An & Liao, Yu-Hsien, 2008. "Potential approach and characterizations of a Shapley value in multi-choice games," Mathematical Social Sciences, Elsevier, vol. 56(3), pages 321-335, November.
    7. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
    8. Yu-Hsien Liao, 2012. "Converse consistent enlargements of the unit-level-core of the multi-choice games," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 20(4), pages 743-753, December.
    9. Branzei, R. & Tijs, S. & Zarzuelo, J., 2009. "Convex multi-choice games: Characterizations and monotonic allocation schemes," European Journal of Operational Research, Elsevier, vol. 198(2), pages 571-575, October.
    10. Brânzei, R. & Tijs, S.H. & Zarzuelo, J., 2007. "Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes," Discussion Paper 2007-54, Tilburg University, Center for Economic Research.
    11. Fanyong Meng & Qiang Zhang & Xiaohong Chen, 0. "Fuzzy Multichoice Games with Fuzzy Characteristic Functions," Group Decision and Negotiation, Springer, vol. 0, pages 1-31.
    12. Txus Ortells & Juan Santos, 2011. "The pseudo-average rule: bankruptcy, cost allocation and bargaining," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 73(1), pages 55-73, February.

    More about this item


    Multi-choice games · Shapley value · characterizations · balanced contributions;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games


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