Ensuring the boundedness of the core of games with restricted cooperation

Michel Grabisch

Post-Print from HAL

Abstract: The core of a cooperative game on a set of players N is one of the most popular concept of solution. When cooperation is restricted (feasible coalitions form a subcollection F of 2N), the core may become unbounded, which makes it usage questionable in practice. Our proposal is to make the core bounded by turning some of the inequalities defining the core into equalities (additional efficiency constraints). We address the following mathematical problem : can we find a minimal set of inequalities in the core such that, if turned into equalities, the core becomes bounded ? The new core obtained is called the restricted core. We completely solve the question when F is a distributive lattice, introducing also the notion of restricted Weber set. We show that the case of regular set systems amounts more or less to the case of distributive lattices. We also study the case of weakly union-closed systems and give some results for the general case.

Keywords: Cooperative game; core; restricted cooperation; bounded core; Weber set; Jeu coopératif; coeur; coopération restreinte; coeur borné; ensemble de Weber (search for similar items in EconPapers)
Date: 2010-11
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00544134v1
References: View references in EconPapers View complete reference list from CitEc
Citations:

Published in 2010

Downloads: (external link)
https://shs.hal.science/halshs-00544134v1/document (application/pdf)

Related works:
Journal Article: Ensuring the boundedness of the core of games with restricted cooperation (2011)
Working Paper: Ensuring the boundedness of the core of games with restricted cooperation (2011)
Working Paper: Ensuring the boundedness of the core of games with restricted cooperation (2011)
Working Paper: Ensuring the boundedness of the core of games with restricted cooperation (2011)
Working Paper: Ensuring the boundedness of the core of games with restricted cooperation (2010)
Working Paper: Ensuring the boundedness of the core of games with restricted cooperation (2010)
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-00544134

Access Statistics for this paper

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