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The Shapley value of conjunctive-restricted games

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  • Derks, Jean

Abstract

We consider transferable utility games, where restricted cooperation is modeled by a fixed mapping assigning to each coalition the set of players that are controlled by this coalition. We study the Shapley value on the resulting class of restricted games, and provide axiomatic frameworks characterizing this value. Studies show that several classes of so-called conjunctive restrictions lead to frameworks similar to the original introduced by Shapley in 1953. We show that conjunctivity of the restriction is not only sufficient but also necessary.

Suggested Citation

  • Derks, Jean, 2018. "The Shapley value of conjunctive-restricted games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 146-151.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:146-151
    DOI: 10.1016/j.geb.2018.01.012
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    References listed on IDEAS

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    1. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    2. René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 47(1), pages 175-188, May.
    3. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    4. Derks, Jean & Peters, Hans, 1993. "A Shapley Value for Games with Restricted Coalitions," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(4), pages 351-360.
    5. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 249-266.
    6. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2011. "Games on Union Closed Systems," Tinbergen Institute Discussion Papers 11-036/1, Tinbergen Institute.
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    More about this item

    Keywords

    Transferable utility games; Restricted cooperation; Shapley value; Axiomatic approach; Conjunctive restriction;
    All these keywords.

    JEL classification:

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

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