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A Core-partition solution for coalitional rankings with a variable population domain

Author

Listed:
  • Sylvain Béal

    (CRESE EA3190, Univ. Bourgogne Franche-Comté, F-25000 Besançon, France)

  • Sylvain Ferrières

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France)

  • Philippe Solal

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, France)

Abstract

A coalitional ranking problem is described by a weak order on the set of nonempty coalitions of a given agent set. A social ranking is a weak order on the set of agents. We consider social rankings that are consistent with stable/core partitions. A partition is stable if there is no coalition better ranked in the coalitional ranking than the rank of the cell of each of its members in the partition. The core-partition social ranking solution assigns to each coalitional ranking problem the set of social rankings such that there is a core-partition satisfying the following condition: a first agent gets a higer rank than a second agent if and only if the cell to which the first agent belongs is better ranked in the coalitional ranking than the cell to which the second agent belongs in the partition. We provide an axiomatic characterization of the core-partition social ranking and an algorithm to compute the associated social rankings.

Suggested Citation

  • Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2021. "A Core-partition solution for coalitional rankings with a variable population domain," Working Papers 2021-06, CRESE.
    • Handle: RePEc:crb:wpaper:2021-06
    as

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    References listed on IDEAS

    as
    1. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(4), pages 817-849, November.
    2. Encarnación Algaba & Stefano Moretti & Eric Rémila & Philippe Solal, 2021. "Lexicographic solutions for coalitional rankings," Post-Print hal-03422945, HAL.
    3. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
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    5. Tayfun Sönmez & Suryapratim Banerjee & Hideo Konishi, 2001. "Core in a simple coalition formation game," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(1), pages 135-153.
    6. Mehmet Karakaya & Bettina Klaus, 2017. "Hedonic coalition formation games with variable populations: core characterizations and (im)possibilities," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(2), pages 435-455, May.
    7. , & ,, 2009. "Coalition formation under power relations," Theoretical Economics, Econometric Society, vol. 4(1), March.
    8. Giulia Bernardi & Roberto Lucchetti & Stefano Moretti, 2019. "Ranking objects from a preference relation over their subsets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 52(4), pages 589-606, April.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Coalitional ranking problem; social ranking; core partition; axiomatic characterization; hedonic games;
    All these keywords.

    JEL classification:

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

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