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Characterizations of a Multi-Choice Value

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  • Klijn, F.

    (Tilburg University, Faculty of Economics)

  • Slikker, M.

    (Tilburg University, Faculty of Economics)

  • Zarzuelo, J.

Abstract

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.
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Suggested Citation

  • Klijn, F. & Slikker, M. & Zarzuelo, J., 1997. "Characterizations of a Multi-Choice Value," Research Memorandum 756, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiurem:fb52ef4b-d73a-486d-b154-f3fc512c5a96
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    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. Larrea, Concepcion & Santos, J.C., 2006. "Cost allocation schemes: An asymptotic approach," Games and Economic Behavior, Elsevier, vol. 57(1), pages 63-72, October.
    2. 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.
    3. GRABISCH, Michel & LABREUCHE, Christophe & RIDAOUI, Mustapha, 2019. "On importance indices in multicriteria decision making," European Journal of Operational Research, Elsevier, vol. 277(1), pages 269-283.
    4. Sylvain Béal & Adriana Navarro-Ramos & Eric Rémila & Philippe Solal, 2023. "Sharing the cost of hazardous transportation networks and the Priority Shapley value," Working Papers hal-04222245, HAL.
    5. 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.
    6. 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.
    7. David Lowing & Kevin Techer, 2022. "Marginalism, egalitarianism and efficiency in multi-choice games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 59(4), pages 815-861, November.
    8. David Lowing, 2023. "Allocation rules for multi-choice games with a permission tree structure," Annals of Operations Research, Springer, vol. 320(1), pages 261-291, January.
    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. David Lowing & Kevin Techer, 2021. "Marginalism, Egalitarianism and E ciency in Multi-Choice Games," Working Papers halshs-03334056, HAL.
    12. Brânzei, R. & Tijs, S.H. & Zarzuelo, J., 2007. "Convex Multi-Choice Cooperative Games and their Monotonic Allocation Schemes," Other publications TiSEM 5549df35-acc3-4890-be43-4, Tilburg University, School of Economics and Management.
    13. 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.
    14. 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.
    15. M. Albizuri, 2009. "The multichoice coalition value," Annals of Operations Research, Springer, vol. 172(1), pages 363-374, November.
    16. 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.
    17. David Lowing & Makoto Yokoo, 2023. "Sharing values for multi-choice games: an axiomatic approach," Working Papers hal-04018735, HAL.
    18. Calvo, Emilio & Santos, Juan Carlos, 2000. "A value for multichoice games," Mathematical Social Sciences, Elsevier, vol. 40(3), pages 341-354, November.
    19. Lowing, David & Techer, Kevin, 2022. "Priority relations and cooperation with multiple activity levels," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    20. Larrea, C. & Santos, J.C., 2007. "A characterization of the pseudo-average cost method," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 140-149, March.

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    More about this item

    Keywords

    game theory;

    JEL classification:

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

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