Games on concept lattices: Shapley value and core

Ulrich Faigle (1) , Michel Grabisch (2, 3) , Andres Jiménez-Losada (4) , Manuel Ordóñez (4)

1 Universität zu Köln = University of Cologne
2 PSE - Paris School of Economics
3 CES - Centre d'économie de la Sorbonne
4 ETSI - Escuela Técnica Superior de Ingenieros de Sevilla

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.

Mots clés: cooperative game; restricted cooperation; concept lattice; core; Shapley value

Domaines: Mathématique discrète [cs.DM]; Economies et finances

Ulrich Faigle, Michel Grabisch, Andres Jiménez-Losada, Manuel Ordóñez. Games on concept lattices: Shapley value and core. Discrete Applied Mathematics, 2016, 198, pp.29 - 47. ⟨10.1016/j.dam.2015.08.004⟩. ⟨hal-01379699⟩