Resource Allocation Problems with Concave Reward Functions

CentER Discussion Paper Series No. 2013-070

15 Pages Posted: 21 Dec 2013 Last revised: 18 Feb 2014

See all articles by Soesja Grundel

Soesja Grundel

Center for Economic Research (CentER) - Tilburg University

Peter Borm

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

Herbert Hamers

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

Date Written: December 19, 2013

Abstract

In a resource allocation problem there is a common-pool resource, which has to be divided among agents. Each agent is characterized by a claim on this pool and an individual concave reward function on assigned resources. An assignment of resources is optimal if the total joint reward is maximized. We provide a necessary and sufficient condition for optimality of an assignment. Analyzing the associated allocation problem of the maximal total joint reward, we consider corresponding resource allocation games. It is shown that these games have a non-empty core and thus allow for stable allocations. Moreover, an explicit expression for the nucleolus of these games is provided.

Keywords: Resource Allocation Games, Concave Reward Function, Core, Nucleolus

JEL Classification: C71

Suggested Citation

Grundel, Soesja and Borm, Peter E. M. and Hamers, Herbert, Resource Allocation Problems with Concave Reward Functions (December 19, 2013). CentER Discussion Paper Series No. 2013-070. Available at SSRN: https://ssrn.com/abstract=2370315 or http://dx.doi.org/10.2139/ssrn.2370315

Soesja Grundel (Contact Author)

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

P.O. Box 90153
Tilburg, DC Noord-Brabant 5000 LE
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

Herbert Hamers

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

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

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