IDEAS home Printed from https://ideas.repec.org/a/eee/matsoc/v57y2009i1p134-142.html
   My bibliography  Save this article

Random assignment of multiple indivisible objects

Author

Listed:
  • Kojima, Fuhito

Abstract

We consider random assignment of multiple indivisible objects. When each agent receives one object, [Bogomolnaia, A., Moulin, H., 2001. A new solution to the random assignment problem. Journal of Economic Theory 100, 295-328] show that the probabilistic serial mechanism is ordinally efficient, envy-free and weakly strategy-proof. When each agent receives more than one object, we propose a generalized probabilistic serial mechanism that is ordinally efficient and envy-free but not weakly strategy-proof. Our main result shows that, if each agent receives more than one object, there exists no mechanism that is ordinally efficient, envy-free and weakly strategy-proof.

Suggested Citation

  • Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
  • Handle: RePEc:eee:matsoc:v:57:y:2009:i:1:p:134-142
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0165-4896(08)00066-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Lars Ehlers & Bettina Klaus, 2003. "Coalitional strategy-proof and resource-monotonic solutions for multiple assignment problems," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 21(2), pages 265-280, October.
    2. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    3. Hervé Crès & Hervé Moulin, 2001. "Scheduling with Opting Out: Improving upon Random Priority," Operations Research, INFORMS, vol. 49(4), pages 565-577, August.
    4. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    5. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, vol. 95(2), pages 368-371, May.
    6. Abdulkadiroglu, Atila & Sonmez, Tayfun, 2003. "Ordinal efficiency and dominated sets of assignments," Journal of Economic Theory, Elsevier, vol. 112(1), pages 157-172, September.
    7. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    8. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    9. Hylland, Aanund & Zeckhauser, Richard, 1979. "The Efficient Allocation of Individuals to Positions," Journal of Political Economy, University of Chicago Press, vol. 87(2), pages 293-314, April.
    10. repec:bla:jpbect:v:3:y:2001:i:3:p:257-71 is not listed on IDEAS
    11. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
    12. Manea, Mihai, 2008. "A constructive proof of the ordinal efficiency welfare theorem," Journal of Economic Theory, Elsevier, vol. 141(1), pages 276-281, July.
    13. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    14. Yan Chen & Tayfun Sönmez, 2002. "Improving Efficiency of On-Campus Housing: An Experimental Study," American Economic Review, American Economic Association, vol. 92(5), pages 1669-1686, December.
    15. McLennan, Andrew, 2002. "Ordinal Efficiency and the Polyhedral Separating Hyperplane Theorem," Journal of Economic Theory, Elsevier, vol. 105(2), pages 435-449, August.
    16. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    17. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    Full references (including those not matched with items on IDEAS)

    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. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    2. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    3. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2209-2226, September.
    4. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    5. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    6. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    7. YIlmaz, Özgür, 2010. "The probabilistic serial mechanism with private endowments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 475-491, July.
    8. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.
    9. Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
    10. Roth, Alvin E. & Sonmez, Tayfun & Utku Unver, M., 2005. "Pairwise kidney exchange," Journal of Economic Theory, Elsevier, vol. 125(2), pages 151-188, December.
    11. Bettina Klaus & David F. Manlove & Francesca Rossi, 2014. "Matching under Preferences," Cahiers de Recherches Economiques du Département d'économie 14.07, Université de Lausanne, Faculté des HEC, Département d’économie.
    12. Morrill, Thayer, 2015. "Making just school assignments," Games and Economic Behavior, Elsevier, vol. 92(C), pages 18-27.
    13. Onur Kesten & Morimitsu Kurino & Alexander S. Nesterov, 2017. "Efficient lottery design," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 31-57, January.
    14. Alexander Nesterov, "undated". "Fairness and Efficiency in a Random Assignment: Three Impossibility Results," BDPEMS Working Papers 2014006, Berlin School of Economics.
    15. Marek Bojko, 2020. "The Probabilistic Serial and Random Priority Mechanisms with Minimum Quotas," Papers 2012.11028, arXiv.org.
    16. Anno, Hidekazu & Kurino, Morimitsu, 2016. "On the operation of multiple matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 166-185.
    17. Thomson, William, 2011. "Chapter Twenty-One - Fair Allocation Rules," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 2, chapter 21, pages 393-506, Elsevier.
    18. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    19. Jose Alcalde & José Ángel Silva-Reus, 2013. "Allocating via Priorities," QM&ET Working Papers 13-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    20. Afacan, Mustafa Oǧuz, 2018. "The object allocation problem with random priorities," Games and Economic Behavior, Elsevier, vol. 110(C), pages 71-89.

    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:eee:matsoc:v:57:y:2009:i:1:p:134-142. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505565 .

    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.