Games on concepts lattices: Shapley value and core

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U. Faigle, M. Grabisch, A. Jiménez-Losada, M. Ordonez
Discrete Applied Mathematics
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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 (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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