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Coalitional substitution of players and the proportional Shapley value

Author

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  • Besner, Manfred

Abstract

We present a new axiomatization of the proportional Shapley Value. Our study is based on three axioms: efficiency, which ensures that the total worth of the grand coalition is fully distributed among the players; the disjointly productive players property, which states that removing a player who has no cooperative interactions with another player does not affect that player's payoff; and a new axiom that makes the difference to the classical Shapley value. This axiom, the coalitional substitution of players property, involves a scenario in which a player's cooperative contribution to a coalition is replaced by that of a group of new players whose combined individual worths match that of the original player. The key point is that the payoffs to the remaining players remain unaffected.

Suggested Citation

  • Besner, Manfred, 2025. "Coalitional substitution of players and the proportional Shapley value," MPRA Paper 123720, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:123720
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    File URL: https://mpra.ub.uni-muenchen.de/123720/1/MPRA_paper_123720.pdf
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    More about this item

    Keywords

    Cooperative game; Proportional Shapley value; Disjointly productive players; Coalitional substitution of players; Patronage refunds;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D60 - Microeconomics - - Welfare Economics - - - General

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