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.
Complete list of metadatas

Cited literature [20 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01379699
Contributor : Michel Grabisch <>
Submitted on : Tuesday, October 11, 2016 - 11:25:36 PM
Last modification on : Monday, April 29, 2019 - 5:44:24 PM
Long-term archiving on : Saturday, February 4, 2017 - 7:23:51 PM

File

conceptlattice-paper3.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

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⟩

Share

Metrics

Record views

237

Files downloads

661