Cost Allocation Rules for Elastic Single-Attribute Situations

CentER Discussion Paper Series No. 2015-016

33 Pages Posted: 6 Mar 2015

See all articles by Frank Karsten

Frank Karsten

Eindhoven University of Technology (TUE)

Marco Slikker

Eindhoven University of Technology (TUE) - School of Industrial Engineering

Peter Borm

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Date Written: March 5, 2015

Abstract

Many cooperative games, especially ones stemming from resource pooling in queuing or inventory systems, are based on situations in which each player is associated with a single attribute (a real number representing, say, a demand) and in which the cost to optimally serve any sum of attributes is described by an elastic function (which means that the per-demand cost is non-increasing in the total demand served). For this class of situations, we introduce and analyze several cost allocation rules: the proportional rule, the serial cost sharing rule, the benefit-proportional rule, and various Shapley-esque rules. We study their appeal with regard to fairness criteria such as coalitional rationality, benefit ordering, and relaxations thereof. After showing the impossibility of combining coalitional rationality and benefit ordering, we show for each of the cost allocation rules which fairness criteria it satisfies.

Keywords: Games/group decisions: cooperative, mathematics: convexity, inventory

JEL Classification: D74, D71

Suggested Citation

Karsten, Frank and Slikker, Marco and Borm, Peter E. M., Cost Allocation Rules for Elastic Single-Attribute Situations (March 5, 2015). CentER Discussion Paper Series No. 2015-016, Available at SSRN: https://ssrn.com/abstract=2574187 or http://dx.doi.org/10.2139/ssrn.2574187

Frank Karsten (Contact Author)

Eindhoven University of Technology (TUE) ( email )

PO Box 513
Eindhoven, 5600 MB
Netherlands

Marco Slikker

Eindhoven University of Technology (TUE) - School of Industrial Engineering ( email )

P.O. Box 513
5600 MB Eindhoven
Netherlands

Peter E. M. Borm

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

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