Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6872000 | Discrete Applied Mathematics | 2016 | 19 Pages |
Abstract
We introduce cooperative TU-games on concept lattices, where a concept is a pair (S,Sâ²) with S being a subset of players or objects, and Sâ² 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.
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Ulrich Faigle, Michel Grabisch, Andres Jiménez-Losada, Manuel Ordóñez,