A new approach to the core and Weber set of multichoice games

Michel Grabisch and Lijue Xie ()
Additional contact information
Lijue Xie: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

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 the set of imputations may be unbounded, which makes its application questionable. A second definition is proposed, imposing normalization at each level, causing the core to be a convex compact 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 coincidence in the convex case remain valid. A last section makes a comparison with the core defined by van den Nouweland et al.

Keywords: multichoice game; lattice; core (search for similar items in EconPapers)
Date: 2007-12
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00267933v1
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (24)

Published in Mathematical Methods of Operations Research, 2007, 66 (3), pp.491-512. ⟨10.1007/s00186-007-0159-8⟩

Downloads: (external link)
https://shs.hal.science/halshs-00267933v1/document (application/pdf)

Related works:
Journal Article: A new approach to the core and Weber set of multichoice games (2007)
Working Paper: A new approach to the core and Weber set of multichoice games (2007)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00267933

DOI: 10.1007/s00186-007-0159-8

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().