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Mixed rules in multi-issue allocation situations

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  • Bergantiños, Gustavo
  • Chamorro, José María
  • Lorenzo, Leticia
  • Lorenzo-Freire, Silvia

Abstract

Multi-issue allocation situations study problems where we have to divide an estate among a group of agents. The claim of each agent is a vector specifying the amount claimed by each agent on each issue. We present a two-stage rule. First we divide the estate among the issues following the constrained equal awards rule. Second, the amount assigned to each issue is divided among the agents proportionally to their demands on this issue. We apply such rule to two real problems: the distribution of natural resources between countries and the distribution of budget for education and research between universities.

Suggested Citation

  • Bergantiños, Gustavo & Chamorro, José María & Lorenzo, Leticia & Lorenzo-Freire, Silvia, 2019. "Mixed rules in multi-issue allocation situations," MPRA Paper 94314, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:94314
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    References listed on IDEAS

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    1. Chun, Youngsub, 1988. "The proportional solution for rights problems," Mathematical Social Sciences, Elsevier, vol. 15(3), pages 231-246, June.
    2. Gautier, Axel & Wauthy, Xavier, 2007. "Teaching versus research: A multi-tasking approach to multi-department universities," European Economic Review, Elsevier, vol. 51(2), pages 273-295, February.
    3. Carlos González-Alcón & Peter Borm & Ruud Hendrickx, 2007. "A composite run-to-the-bank rule for multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 65(2), pages 339-352, April.
    4. Rey, Elena Del, 2001. "Teaching versus Research: A Model of State University Competition," Journal of Urban Economics, Elsevier, vol. 49(2), pages 356-373, March.
    5. Juan D. Moreno-Ternero, 2009. "The proportional rule for multi-issue bankruptcy problems," Economics Bulletin, AccessEcon, vol. 29(1), pages 474-481.
    6. Ju, Biung-Ghi & Miyagawa, Eiichi & Sakai, Toyotaka, 2007. "Non-manipulable division rules in claim problems and generalizations," Journal of Economic Theory, Elsevier, vol. 132(1), pages 1-26, January.
    7. Calleja, Pedro & Borm, Peter & Hendrickx, Ruud, 2005. "Multi-issue allocation situations," European Journal of Operational Research, Elsevier, vol. 164(3), pages 730-747, August.
    8. Thomson, William & Yeh, Chun-Hsien, 2008. "Operators for the adjudication of conflicting claims," Journal of Economic Theory, Elsevier, vol. 143(1), pages 177-198, November.
    9. Fandel, Gunter & Gal, Tomas, 2001. "Redistribution of funds for teaching and research among universities: The case of North Rhine-Westphalia," European Journal of Operational Research, Elsevier, vol. 130(1), pages 111-120, April.
    10. 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.
    11. Carmen Herrero & Antonio Villar, 2002. "Sustainability in bankruptcy problems," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 261-273, December.
    12. Gustavo Bergantiños & Leticia Lorenzo & Silvia Lorenzo-Freire, 2011. "New characterizations of the constrained equal awards rule in multi-issue allocation situations," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 74(3), pages 311-325, December.
    13. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
    14. Chun-Hsien Yeh, 2006. "Protective Properties and the Constrained Equal Awards Rule for Claims Problems: A Note," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 27(2), pages 221-230, October.
    15. Thomson, William, 2015. "Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update," Mathematical Social Sciences, Elsevier, vol. 74(C), pages 41-59.
    16. Lorenzo-Freire, S. & Alonso-Meijide, J.M. & Casas-Mendez, B. & Hendrickx, R.L.P., 2005. "Balanced Contributions for Multi-Issue Allocation Situations," Discussion Paper 2005-93, Tilburg University, Center for Economic Research.
    17. Silvia Lorenzo-Freire & Balbina Casas-Méndez & Ruud Hendrickx, 2010. "The two-stage constrained equal awards and losses rules for multi-issue allocation situations," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(2), pages 465-480, December.
    18. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
    19. 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.
    20. Ershad Oftadeh & Mojtaba Shourian & Bahram Saghafian, 2016. "Evaluation of the Bankruptcy Approach for Water Resources Allocation Conflict Resolution at Basin Scale, Iran’s Lake Urmia Experience," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3519-3533, August.
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    Cited by:

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    3. J. Sánchez-Pérez, 2023. "New results for multi-issue allocation problems and their solutions," Review of Economic Design, Springer;Society for Economic Design, vol. 27(2), pages 313-336, June.

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    More about this item

    Keywords

    multi-issue allocation situations; proportional rule; constrained equal awards rule;
    All these keywords.

    JEL classification:

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

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