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A Core-Partition Ranking Solution to Coalitional Ranking Problems

Author

Listed:
  • Sylvain Béal

    (UFC - Université de Franche-Comté - UBFC - Université Bourgogne Franche-Comté [COMUE])

  • Sylvain Ferrières

    (UJM - Université Jean Monnet - Saint-Étienne)

  • Philippe Solal

    (UJM - Université Jean Monnet - Saint-Étienne)

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 higher 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.
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Suggested Citation

  • Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2023. "A Core-Partition Ranking Solution to Coalitional Ranking Problems," Post-Print hal-04114152, HAL.
    • Handle: RePEc:hal:journl:hal-04114152
    DOI: 10.1007/s10726-023-09832-2
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    References listed on IDEAS

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    JEL classification:

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

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