Games on concept lattices: Shapley value and core

Abstract : 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 (non-emptiness, boundedness, pointedness, extremal rays). In particular, we derive the equivalence of the intent and extent core for the class of distributive concepts.
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Contributor : Michel Grabisch <>
Submitted on : Tuesday, October 11, 2016 - 11:25:36 PM
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Ulrich Faigle, Michel Grabisch, Andres Jiménez-Losada, Manuel Ordóñez. Games on concept lattices: Shapley value and core. Discrete Applied Mathematics, Elsevier, 2016, 198, pp.29 - 47. ⟨10.1016/j.dam.2015.08.004⟩. ⟨hal-01379699⟩



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