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Mathematical Methods of Operations Research
Article . 2000 . Peer-reviewed
License: Springer TDM
Data sources: Crossref
image/svg+xml Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao Closed Access logo, derived from PLoS Open Access logo. This version with transparent background. http://commons.wikimedia.org/wiki/File:Closed_Access_logo_transparent.svg Jakob Voss, based on art designer at PLoS, modified by Wikipedia users Nina and Beao
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Data sources: zbMATH Open
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Article . 2000
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The proportional value for positive cooperative games

Authors: K. Michael Ortmann;

The proportional value for positive cooperative games

Abstract

By generalizing in a natural way the idea of proportional division of surplus for two person games, a new solution concept for TU cooperative games is introduced and called the proportional value. Its domain is restricted to strictly positive games but, as is noticed, this solution applies as well to strictly negative games. A motivating example is given in Section 1. In Section 2 it is first shown that a value admits a (multiplicative) potential if, and only if, it preserves ratios -- a proportionally balanced contribution property. Next two axiomatic characterizations are provided for the proportional value: the first one, in terms of efficiency and ratio preservation; the second, by means of proportionality for two person games and consistency with regard to a classical notion of reduced game. For computation purposes, two recursive formulae concerning the potential are supplied in Section 3. Finally, several further properties of the proportional value are shown in Section 4: homogeneity, monotonicity, the dummy player property, anonymity and the inessential game property. Perhaps it should have been also mentioned that the proportional value fails to satisfy additivity, as this may cause some trouble when trying to evaluate, e.g., a discount problem in terms of both cost and saving share. Of course, the paper will be of interest to mathematicians (cooperative game theorists) and economists.

Keywords

potential, Cooperative games, consistency, proportional value, contributions, balanced, Shapley value

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
44
Top 10%
Top 10%
Average
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