Games on lattices, multichoice games and the Shapley value: a new approach

Abstract : Multichoice games have been introduced by Hsiao and Raghavan as a generalization of classical cooperative games. An important notion in cooperative game theory is the core of the game, as it contains the rational imputations for players. We propose two definitions for the core of a multichoice game, the first one is called the precore and is a direct generalization of the classical definition. We show that the precore coincides with the definition proposed by Faigle, and that it contains unbounded imputations, which makes its application questionable. A second definition is proposed, imposing normalization at each level, causing the core to be a convex closed set. We study its properties, introducing balancedness and marginal worth vectors, and defining the Weber set and the pre-Weber set. We show that the classical properties of inclusion of the (pre)core into the (pre)-Weber set as well as their equality remain valid. A last section makes a comparison with the core defined by van den Nouweland et al.
Complete list of metadatas

Cited literature [19 references]  Display  Hide  Download

https://halshs.archives-ouvertes.fr/halshs-00178916
Contributor : Michel Grabisch <>
Submitted on : Friday, October 12, 2007 - 2:40:56 PM
Last modification on : Tuesday, March 27, 2018 - 11:48:05 AM
Long-term archiving on : Sunday, April 11, 2010 - 10:54:33 PM

File

mmor05.pdf
Files produced by the author(s)

Identifiers

Collections

Citation

Michel Grabisch, Fabien Lange. Games on lattices, multichoice games and the Shapley value: a new approach. Mathematical Methods of Operations Research, Springer Verlag, 2007, 65 (1), pp.153-167. ⟨10.1007/s00186-006-0109-x⟩. ⟨halshs-00178916⟩

Share

Metrics

Record views

371

Files downloads

448