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New axiomatizations of the Diversity Owen and Shapley values

Author

Listed:
  • Sylvain Béal

    (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France)

  • Mostapha Diss

    (Université de Franche-Comté, CRESE, UR3190, F-25000 Besançon, France)

  • Rodrigue Tido Takeng

    (Université de Caen, CREM, UMR6211, F-14000 Caen, France)

Abstract

The Shapley and Owen values defined respectively for cooperative games with transferable utility (TU-games), and TU-games with coalition structure have recently been extended as allocation rules for TU-games with diversity constraints. This new class of games is introduced by B ́eal et al. (Working paper, 2024). In this new environment, players are divided into disjointed groups called communities. Diversity constraints require a mini- mum number of members in each community for cooperation to take place. A coalition is diverse if it contains at least the required number of members from each community. The diversity-restricted game is a TU-game which assigns zero to any non-diverse coalition and also assigns the original worth of a coalition if it is diverse. The extensions of the Shapley and Owen values are respectively called the Diversity Shapley value which is defined as the Shapley value of the diversity-restricted game, and the Diversity Owen value which is defined as the Owen value of the diversity-restricted game with coalition structure. Moreover, two axiomatic characterizations of these values are given. In this paper, we also present two new axiomatic characterizations of the Diversity Owen and Shapley values.

Suggested Citation

  • Sylvain Béal & Mostapha Diss & Rodrigue Tido Takeng, 2024. "New axiomatizations of the Diversity Owen and Shapley values," Working Papers 2024-09, CRESE.
    • Handle: RePEc:crb:wpaper:2024-09
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    References listed on IDEAS

    as
    1. René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 309-319.
    2. Chun, Youngsub, 1991. "On the Symmetric and Weighted Shapley Values," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(2), pages 183-190.
    3. Roger B. Myerson, 1977. "Graphs and Cooperation in Games," Mathematics of Operations Research, INFORMS, vol. 2(3), pages 225-229, August.
    4. André Casajus, 2010. "Another characterization of the Owen value without the additivity axiom," Theory and Decision, Springer, vol. 69(4), pages 523-536, October.
    5. Chun, Youngsub, 1989. "A new axiomatization of the shapley value," Games and Economic Behavior, Elsevier, vol. 1(2), pages 119-130, June.
    6. AUMANN, Robert J. & DREZE, Jacques H., 1974. "Cooperative games with coalition structures," LIDAM Reprints CORE 217, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    TU-games; diversity constraints; axiomatic characterization; Diversity Shapley value; Diversity Owen value.;
    All these keywords.

    JEL classification:

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

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