Resource Allocation Problems with Concave Reward Functions

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Abstract

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.
Original languageEnglish
Place of PublicationTilburg
PublisherOperations research
Number of pages15
Volume2013-070
Publication statusPublished - 2013

Publication series

NameCentER Discussion Paper
Volume2013-070

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Keywords

  • Resource Allocation Games
  • Concave Reward Function
  • Core
  • Nucleolus

Cite this

Grundel, S., Borm, P. E. M., & Hamers, H. J. M. (2013). Resource Allocation Problems with Concave Reward Functions. (CentER Discussion Paper; Vol. 2013-070). Tilburg: Operations research.