Weighted allocation rules for standard fixed tree games

Endre Jostein Bjørndal, Maurice Koster () and Stef Tijs ()

Mathematical Methods of Operations Research, 2004, vol. 59, issue 2, 249-270

Abstract: In this paper we consider standard fixed tree games, for which each vertex unequal to the root is inhabited by exactly one player. We present two weighted allocation rules, the weighted down-home allocation and the weighted neighbour-home allocation, both inspired by the painting story in Maschler et al. (1995) . We show, in a constructive way, that the core equals both the set of weighted down-home allocations and the set of weighted neighbour allocations. Since every weighted down-home allocation specifies a weighted Shapley value (Kalai and Samet (1988)) in a natural way, and vice versa, our results provide an alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the special member where players have all equal weights. Copyright Springer-Verlag 2004

Keywords: Cooperative games; Tree games; Core; Weighted Shapley value; Nucleolus (search for similar items in EconPapers)
Date: 2004
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s001860300324 (text/html)
Access to full text is restricted to subscribers.

Related works:
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:59:y:2004:i:2:p:249-270

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/00186

DOI: 10.1007/s001860300324

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 ().