On the restricted cores and the bounded core of games on distributive lattices

Abstract : A game with precedence constraints is a TU game with restricted cooperation, where the set of feasible coalitions is a distributive lattice, hence generated by a partial order on the set of players. Its core may be unbounded, and the bounded core, which is the union of all bounded faces of the core, proves to be a useful solution concept in the framework of games with precedence constraints. Replacing the inequalities that define the core by equations for a collection of coalitions results in a face of the core. A collection of coalitions is called normal if its resulting face is bounded. The bounded core is the union of all faces corresponding to minimal normal collections. We show that two faces corresponding to distinct normal collections may be distinct. Moreover, we prove that for superadditive games and convex games only intersecting and nested minimal collection, respectively, are necessary. Finally, it is shown that the faces corresponding to pairwise distinct nested normal collections may be pairwise distinct, and we provide a means to generate all such collections.
Complete list of metadatas

Cited literature [29 references]  Display  Hide  Download

https://halshs.archives-ouvertes.fr/halshs-00950109
Contributor : Michel Grabisch <>
Submitted on : Thursday, February 20, 2014 - 5:48:16 PM
Last modification on : Friday, July 26, 2019 - 11:58:03 AM
Long-term archiving on : Tuesday, May 20, 2014 - 3:51:18 PM

File

restrictedcore3R1-p.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Michel Grabisch, Peter Sudhölter. On the restricted cores and the bounded core of games on distributive lattices. European Journal of Operational Research, Elsevier, 2014, 235 (3), pp.709-717. ⟨10.1016/j.ejor.2013.10.027⟩. ⟨halshs-00950109⟩

Share

Metrics

Record views

856

Files downloads

417