IDEAS home Printed from https://ideas.repec.org/p/tiu/tiutis/b72ed3dc-ecc8-49d4-86af-d4598cb9ddfd.html
   My bibliography  Save this paper

Resource Allocation Problems with Concave Reward Functions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://pure.uvt.nl/ws/portalfiles/portal/1560085/2013-070a.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    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.
    3. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    4. Carlo Carraro & Carmen Marchiori & Alessandra Sgobbi, 2005. "Applications of Negotiation Theory to Water Issues," Working Papers 2005.65, Fondazione Eni Enrico Mattei.
    5. Parrachino, Irene & Dinar, Ariel & Patrone, Fioravante, 2006. "Cooperative game theory and its application to natural, environmental, and water resource issues : 3. application to water resources," Policy Research Working Paper Series 4074, The World Bank.
    6. Condorelli, Daniele, 2013. "Market and non-market mechanisms for the optimal allocation of scarce resources," Games and Economic Behavior, Elsevier, vol. 82(C), pages 582-591.
    7. Harris Milton & Townsend, Robert M, 1981. "Resource Allocation under Asymmetric Information," Econometrica, Econometric Society, vol. 49(1), pages 33-64, January.
    8. van den Brink, René & van der Laan, Gerard & Moes, Nigel, 2012. "Fair agreements for sharing international rivers with multiple springs and externalities," Journal of Environmental Economics and Management, Elsevier, vol. 63(3), pages 388-403.
    9. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    10. Palvolgyi, D.G. & Peters, H.J.M. & Vermeulen, A.J., 2010. "A strategic approach to estate division problems with non-homogenous preferences," Research Memorandum 036, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    11. Wang, Yuntong, 2011. "Trading water along a river," Mathematical Social Sciences, Elsevier, vol. 61(2), pages 124-130, March.
    12. Zara, Stefano & Dinar, Ariel & Patrone, Fioravante, 2006. "Cooperative game theory and its application to natural, environmental, and water resource issues : 2. application to natural and environmental resources," Policy Research Working Paper Series 4073, The World Bank.
    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.
    14. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Grundel, S. & Borm, P.E.M. & Hamers, H.J.M., 2011. "A Compromise Stable Extension of Bankruptcy Games : Multipurpose Resource Allocation," Other publications TiSEM b1926d6b-22f4-4f28-84a2-9, Tilburg University, School of Economics and Management.
    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.
    3. van den Brink, René & He, Simin & Huang, Jia-Ping, 2018. "Polluted river problems and games with a permission structure," Games and Economic Behavior, Elsevier, vol. 108(C), pages 182-205.
    4. Hurt, Wesley & Osório, António (António Miguel), 2014. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," Working Papers 2072/237596, Universitat Rovira i Virgili, Department of Economics.
    5. Dongshuang Hou & Aymeric Lardon & Panfei Sun & Genjiu Xu, 2019. "Sharing a Polluted River under Waste Flow Control," GREDEG Working Papers 2019-23, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
    6. René Brink & Arantza Estévez-Fernández & Gerard Laan & Nigel Moes, 2014. "Independence of downstream and upstream benefits in river water allocation problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(1), pages 173-194, June.
    7. Osório, António (António Miguel), 2016. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," Working Papers 2072/266574, Universitat Rovira i Virgili, Department of Economics.
    8. António Osório, 2017. "A Sequential Allocation Problem: The Asymptotic Distribution of Resources," Group Decision and Negotiation, Springer, vol. 26(2), pages 357-377, March.
    9. Gerard van der Laan & Nigel Moes, 2012. "Transboundary Externalities and Property Rights: An International River Pollution Model," Tinbergen Institute Discussion Papers 12-006/1, Tinbergen Institute.
    10. René van den Brink & Simin He & Jia-Ping Huang, 2015. "Polluted River Problems and Games with a Permission Structure," Tinbergen Institute Discussion Papers 15-108/II, Tinbergen Institute.
    11. Hadi Tarebari & Amir Hossein Javid & Seyyed Ahmad Mirbagheri & Hedayat Fahmi, 2018. "Multi-Objective Surface Water Resource Management Considering Conflict Resolution and Utility Function Optimization," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(14), pages 4487-4509, November.
    12. Lea Melnikovová, 2017. "Can Game Theory Help to Mitigate Water Conflicts in the Syrdarya Basin?," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 65(4), pages 1393-1401.
    13. M. Fiestras-Janeiro & Ignacio García-Jurado & Manuel Mosquera, 2011. "Cooperative games and cost allocation problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-22, July.
    14. Ambec, Stefan & Dinar, Ariel & McKinney, Daene, 2013. "Water sharing agreements sustainable to reduced flows," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 639-655.
    15. Dagmawi Mulugeta Degefu & Weijun He, 2016. "Allocating Water under Bankruptcy Scenario," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(11), pages 3949-3964, September.
    16. Ansink, Erik & Gengenbach, Michael & Weikard, Hans-Peter, 2012. "River Sharing and Water Trade," Climate Change and Sustainable Development 122860, Fondazione Eni Enrico Mattei (FEEM).
    17. Takayuki Oishi, 2018. "Legal and Political Agreements for Sharing International Rivers with Water Shortage," Discussion Papers 39, Meisei University, School of Economics.
    18. László Á. Kóczy, 2018. "Partition Function Form Games," Theory and Decision Library C, Springer, number 978-3-319-69841-0, July.
    19. Dagmawi Mulugeta Degefu & Weijun He & Liang Yuan, 2017. "Monotonic Bargaining Solution for Allocating Critically Scarce Transboundary Water," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 31(9), pages 2627-2644, July.
    20. Erik Ansink & Harold Houba, 2014. "The Economics of Transboundary River Management," Tinbergen Institute Discussion Papers 14-132/VIII, Tinbergen Institute.

    More about this item

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:tiu:tiutis:b72ed3dc-ecc8-49d4-86af-d4598cb9ddfd. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Richard Broekman (email available below). General contact details of provider: https://www.tilburguniversity.edu/about/schools/economics-and-management/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.