Player splitting, players merging, the Shapley set value and the Harsanyi set value

Manfred Besner

MPRA Paper from University Library of Munich, Germany

Abstract: Shapley (1953a) introduced the weighted Shapley values as a family of values, also known as Shapley set. For each exogenously given weight system exists a seperate TU-value. Shapley (1981) and Dehez (2011), in the context of cost allocation, and Radzik (2012), in general, presented a value for weighted TU-games that covers the hole family of weighted Shapley values all at once. To distinguish this value from a weighted Shapley value in TU-games we call it Shapley set value. This value coincides with a weighted Shapley value only on a subdomain and allows weights which can depend on coalition functions. Hammer (1977) and Vasil’ev (1978) introduced independently the Harsanyi set, also known as selectope (Derks, Haller and Peters, 2000), containing TU-values which are referred to as Harsanyi-payoffs. These values are obtained by distributing the dividends from all coalitions by a sharing system that is independent from the coalition function. In this paper we introduce the Harsanyi set value that, similar to the Shapley set value, covers the hole family of Harsanyi payoffs at once, allows not exogenously given share systems and coincides thus also with non linear values on some subdomains. We present some new axiomatizations of the Shapley set value and the Harsanyi set value containing a player splitting or a players merging property respectively as a main characterizing element that recommend these values for profit distribution and cost allocation.

Keywords: Cost; allocation; ·; Profit; distribution; ·; Player; splitting; ·; Players; merging; ·; Shapley; set; value; ·; Harsanyi; set; value (search for similar items in EconPapers)
JEL-codes: C70 C71 (search for similar items in EconPapers)
Date: 2018-06-01
New Economics Papers: this item is included in nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://mpra.ub.uni-muenchen.de/87125/1/MPRA_paper_87125.pdf original version (application/pdf)
https://mpra.ub.uni-muenchen.de/89201/1/MPRA_paper_89201.pdf revised version (application/pdf)

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:pra:mprapa:87125

Access Statistics for this paper

More papers in MPRA Paper from University Library of Munich, Germany Ludwigstraße 33, D-80539 Munich, Germany. Contact information at EDIRC.
Bibliographic data for series maintained by Joachim Winter ().