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Games on concept lattices: Shapley value and core

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We introduce cooperative TU-games on concept lattices, where a concept is a pair (S,S') with S being a subset of players or objects, and S' a subset of attributes. Any such game induces a game on the set of players/objects, which appears to be a TU-game whose collection of feasible coalitions is a lattice closed under intersection, and a game on the set of attributes. We propose a Shapley value for each type of game, axiomatize it, and investigate the geometrical properties of the core (nonemptiness, boundedness, pointedness, extremal rays)

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  • Ulrich Faigle & Michel Grabisch & Andres Jiménez-Losada & Manuel Ordóñez, 2014. "Games on concept lattices: Shapley value and core," Documents de travail du Centre d'Economie de la Sorbonne 14070, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:14070
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    1. Monjardet, Bernard, 2003. "The presence of lattice theory in discrete problems of mathematical social sciences. Why," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 103-144, October.
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    10. Nathalie Caspard & Bruno Leclerc & Bernard Monjardet, 2012. "Finite Ordered Sets Concepts, Results and Uses," Post-Print halshs-00800193, HAL.
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    Cited by:

    1. Michel Grabisch, 2016. "Remarkable polyhedra related to set functions, games and capacities," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(2), pages 301-326, July.
    2. Surajit Borkotokey & Loyimee Gogoi & Dhrubajit Choudhury & Rajnish Kumar, 2022. "Solidarity induced by group contributions: the MI $$^k$$ k -value for transferable utility games," Operational Research, Springer, vol. 22(2), pages 1267-1290, April.
    3. Ren, Hongbo & Wu, Qiong & Li, Qifen & Yang, Yongwen, 2020. "Optimal design and management of distributed energy network considering both efficiency and fairness," Energy, Elsevier, vol. 213(C).
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    5. Wu, Qiong & Ren, Hongbo & Gao, Weijun & Ren, Jianxing & Lao, Changshi, 2017. "Profit allocation analysis among the distributed energy network participants based on Game-theory," Energy, Elsevier, vol. 118(C), pages 783-794.

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    More about this item

    Keywords

    Cooperation game; restricted cooperation; concept lattice; core; Shapley value;
    All these keywords.

    JEL classification:

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

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