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New axiomatisations of the Diversity Owen and Shapley values

Author

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  • Sylvain Béal

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Mostapha Diss

    (CRESE - Centre de REcherches sur les Stratégies Economiques (UR 3190) - UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE], AIRESS - Africa Institute for Research in Economics and Social Sciences)

  • Rodrigue Tido Takeng

    (UNICAEN - Université de Caen Normandie - NU - Normandie Université)

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 coali- tion 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 axiomatisations of the Diversity Owen and Shapley values," Working Papers hal-04502031, HAL.
    • Handle: RePEc:hal:wpaper:hal-04502031
    Note: View the original document on HAL open archive server: https://hal.science/hal-04502031v1
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    2. Béal, Sylvain & Deschamps, Marc & Diss, Mostapha & Tido Takeng, Rodrigue, 2025. "Cooperative games with diversity constraints," Journal of Mathematical Economics, Elsevier, vol. 116(C).

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    JEL classification:

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

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