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Resource Allocation Problems with Concave Reward Functions

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  • Grundel, S.

    (Tilburg University, School of Economics and Management)

  • Borm, P.E.M.

    (Tilburg University, School of Economics and Management)

  • Hamers, H.J.M.

    (Tilburg University, School of Economics and Management)

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Grundel, S. & Borm, P.E.M. & Hamers, H.J.M., 2013. "Resource Allocation Problems with Concave Reward Functions," Other publications TiSEM b72ed3dc-ecc8-49d4-86af-d, Tilburg University, School of Economics and Management.
    • Handle: RePEc:tiu:tiutis:b72ed3dc-ecc8-49d4-86af-d4598cb9ddfd
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    References listed on IDEAS

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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.
    2. Erik Ansink & Hans-Peter Weikard, 2012. "Sequential sharing rules for river sharing problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 38(2), pages 187-210, February.
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    13. Potters, J.A.M. & Tijs, S.H., 1994. "On the locus of the nucleolus," Other publications TiSEM 46039298-9223-44b3-9a3d-c, Tilburg University, School of Economics and Management.
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    Cited by:

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    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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    JEL classification:

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

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