A new approach to the core and Weber set of multichoice games
Michel Grabisch and
Lijue Xie ()
Mathematical Methods of Operations Research, 2007, vol. 66, issue 3, 512 pages
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. Copyright Springer-Verlag 2007
Keywords: Multichoice game; Lattice; Core (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (25)
Downloads: (external link)
http://hdl.handle.net/10.1007/s00186-007-0159-8 (text/html)
Access to full text is restricted to subscribers.
Related works:
Working Paper: 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:spr:mathme:v:66:y:2007:i:3:p:491-512
Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186
DOI: 10.1007/s00186-007-0159-8
Access Statistics for this article
Mathematical Methods of Operations Research is currently edited by Oliver Stein
More articles in Mathematical Methods of Operations Research from Springer, Gesellschaft für Operations Research (GOR), Nederlands Genootschap voor Besliskunde (NGB)
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().