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Resource allocation problems with concave reward functions

Author

Listed:
  • Soesja Grundel

    (CZ Healthcare, Department Operations)

  • Peter Borm

    (Tilburg University)

  • Herbert Hamers

    (Tilburg University)

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, thus generalizing the model of Grundel et al. (Math Methods Oper Res 78(2):149–169, 2013) with linear reward functions. 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, based on bilateral transfers of resources only. Analyzing the associated allocation problem of the maximal total joint reward, we consider corresponding resource allocation games. It is shown that the core and the nucleolus of a resource allocation game are equal to the core and the nucleolus of an associated bankruptcy game.

Suggested Citation

  • Soesja Grundel & Peter Borm & Herbert Hamers, 2019. "Resource allocation problems with concave reward functions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 37-54, April.
    • Handle: RePEc:spr:topjnl:v:27:y:2019:i:1:d:10.1007_s11750-018-0482-7
    DOI: 10.1007/s11750-018-0482-7
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    1. Soesja Grundel & Peter Borm & Herbert Hamers, 2013. "Resource allocation games: a compromise stable extension of bankruptcy games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 149-169, October.
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    Cited by:

    1. Jin Li & Sang-Chul Suh & Yuntong Wang, 2020. "Sharing pollution permits under welfare upper bounds," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(2), pages 489-505, July.
    2. Soesja Grundel & Peter Borm & Herbert Hamers, 2013. "Resource allocation games: a compromise stable extension of bankruptcy games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 78(2), pages 149-169, October.

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    More about this item

    Keywords

    Resource allocation games; Concave reward function; Core; Nucleolus;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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