Ensuring the boundedness of the core of games with restricted cooperation

Michel Grabisch

Annals of Operations Research, 2011, vol. 191, issue 1, 137-154

Abstract: The core of a cooperative game on a set of players N is one of the most popular concepts of solution. When cooperation is restricted (feasible coalitions form a subcollection $\mathcal{F}$ of 2 N ), the core may become unbounded, which makes its 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 $\mathcal{F}$ 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. Copyright Springer Science+Business Media, LLC 2011

Keywords: Cooperative game; Core; Restricted cooperation; Bounded core; Weber set (search for similar items in EconPapers)
Date: 2011
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (30)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-011-0920-5 (text/html)
Access to full text is restricted to subscribers.

Related works:
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)
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:spr:annopr:v:191:y:2011:i:1:p:137-154:10.1007/s10479-011-0920-5

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-011-0920-5

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

More articles in Annals of Operations Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().