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Resource allocation games: a compromise stable extension of bankruptcy games

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  • Soesja Grundel
  • Peter Borm
  • Herbert Hamers

Abstract

This paper presents an extension of the traditional bankruptcy problem. In a resource allocation problem there is a common-pool resource, which needs to be divided among agents. Each agent is characterized by a claim on this pool and an individual linear monetary reward function for assigned resources. Analyzing these problems a new class of transferable utility games is introduced, called resource allocation games. These games are based on the bankruptcy model, as introduced by O’Neill (Math Soc Sci 2:345–371, 1982 ). It is shown that the properties of totally balancedness and compromise stability can be extended to resource allocation games, although the property of convexity is not maintained in general. Moreover, an explicit expression for the nucleolus of these games is provided. Copyright Springer-Verlag Berlin Heidelberg 2013

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  • 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.
    • Handle: RePEc:spr:mathme:v:78:y:2013:i:2:p:149-169
    DOI: 10.1007/s00186-013-0437-6
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    1. Carlo Carraro & Carmen Marchiori & Alessandra Sgobbi, 2005. "Applications of Negotiation Theory to Water Issues," Working Papers 2005.65, Fondazione Eni Enrico Mattei.
    2. 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.
    3. Peter Borm & Herbert Hamers & Ruud Hendrickx, 2001. "Operations research games: A survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 9(2), pages 139-199, December.
    4. Moulin,Hervi, 1991. "Axioms of Cooperative Decision Making," Cambridge Books, Cambridge University Press, number 9780521424585.
    5. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    6. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
    7. Thomson, William, 2003. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey," Mathematical Social Sciences, Elsevier, vol. 45(3), pages 249-297, July.
    8. 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).
    9. 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.
    10. 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.
    11. Marieke Quant & Peter Borm & Hans Reijnierse & Bas van Velzen, 2005. "The core cover in relation to the nucleolus and the Weber set," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(4), pages 491-503, November.
    12. 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.
    13. Tijs, S.H. & Lipperts, F.A.S., 1982. "The hypercube and the core cover of N-person cooperative games," Other publications TiSEM f86cf523-f36d-4652-b774-6, Tilburg University, School of Economics and Management.
    14. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    15. 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.
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    1. 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.
    2. Dagmawi Mulugeta Degefu & Weijun He & Liang Yuan & An Min & Qi Zhang, 2018. "Bankruptcy to Surplus: Sharing Transboundary River Basin’s Water under Scarcity," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 32(8), pages 2735-2751, June.
    3. 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.

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