Games on concept lattices: Shapley value and core

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).