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The Priority Value for Cooperative Games with a Priority Structure

Author

Listed:
  • Sylvain Béal

    (CRESE, Université de Franche-comté)

  • Sylvain Ferrières

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

  • Philippe Solal

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

Abstract

We study cooperative games with a priority structure modeled by a poset on the agent set. We introduce the Priority value, which splits the Harsanyi dividend of each coalition among the set of its priority agents, i.e. the members of the coalition over which no other coalition member has priority. This allocation shares many desirable properties with the classical Shapley value: it is efficient, additive and satisfies the null agent axiom, which assigns a null payoff to any agent with null contributions to coalitions. We provide two axiomatic characterizations of the Priority value which invoke both classical axioms and new axioms describing various effects that the priority structure can impose on the payoff allocation. Applications to queueing and bankruptcy problems are discussed.

Suggested Citation

  • Sylvain Béal & Sylvain Ferrières & Philippe Solal, 2020. "The Priority Value for Cooperative Games with a Priority Structure," Working Papers 2020-02, CRESE.
  • Handle: RePEc:crb:wpaper:2020-02
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    References listed on IDEAS

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    Cited by:

    1. David Lowing, 2023. "Allocation rules for multi-choice games with a permission tree structure," Annals of Operations Research, Springer, vol. 320(1), pages 261-291, January.
    2. Lowing, David & Techer, Kevin, 2022. "Priority relations and cooperation with multiple activity levels," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    3. Sylvain Béal & Sylvain Ferrières & Adriana Navarro‐Ramos & Philippe Solal, 2023. "Axiomatic characterizations of the family of Weighted priority values," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(4), pages 787-816, December.

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    More about this item

    Keywords

    Priority structure; Shapley value; Priority value; necessary agent; Harsanyi solution; queueing problems; bankruptcy problems.;
    All these keywords.

    JEL classification:

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

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