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 (nonemptiness, boundedness, pointedness, extremal rays).
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Ulrich Faigle, Michel Grabisch, Andres Jiménez-Losada, Manuel Ordóñez. Games on concept lattices: Shapley value and core. 2014. ⟨hal-01111670⟩

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