IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v82y2013icp1-14.html
   My bibliography  Save this article

Efficient resource allocation under multi-unit demand

Author

Listed:
  • Kojima, Fuhito

Abstract

We study resource allocation with multi-unit demand, such as the allocation of courses to students. In contrast to the case of single-unit demand, no stable mechanism, not even the (student-proposing) deferred acceptance algorithm, achieves desirable properties: it is not strategy-proof and the resulting allocation is not even weakly efficient under submitted preferences. We characterize the priority structure of courses over students under which stability is consistent with strategy-proofness or efficiency. We show that stability is compatible with strategy-proofness or efficiency if and only if the priority structure is essentially homogeneous. This result suggests that efficient allocation under multi-unit demand is difficult and that the use of stable mechanisms may not deliver desirable outcomes.

Suggested Citation

  • Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
  • Handle: RePEc:eee:gamebe:v:82:y:2013:i:c:p:1-14 DOI: 10.1016/j.geb.2013.06.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899825613000870
    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. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, pages 1860-1874.
    2. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, pages 106-123.
    3. 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.
    4. Onur Kesten, 2012. "On two kinds of manipulation for school choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 677-693.
    5. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," American Economic Review, American Economic Association, pages 2237-2271.
    6. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, pages 729-747.
    7. Aradhna Krishna & M. Utku Ünver, 2008. "Research Note—Improving the Efficiency of Course Bidding at Business Schools: Field and Laboratory Studies," Marketing Science, INFORMS, pages 262-282.
    8. Parag A. Pathak & Tayfun Sönmez, 2013. "School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation," American Economic Review, American Economic Association, pages 80-106.
    9. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    10. Kojima, Fuhito, 2011. "Robust stability in matching markets," Theoretical Economics, Econometric Society.
    11. John Hatfield & Fuhito Kojima & Yusuke Narita, 2012. "Promoting School Competition Through School Choice: A Market Design Approach," Discussion Papers 12-019, Stanford Institute for Economic Policy Research.
    12. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, pages 1921-1947.
    13. Bettina-Elisabeth Klaus & Markus Walzl, 2007. "Stable Many-to-Many Matchings with Contracts," Harvard Business School Working Papers 09-046, Harvard Business School, revised Sep 2008.
    14. Tayfun Sönmez & M. Utku Ünver, 2010. "Course Bidding At Business Schools," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 51(1), pages 99-123, February.
    15. Echenique, Federico & Oviedo, Jorge, 2006. "A theory of stability in many-to-many matching markets," Theoretical Economics, Econometric Society, pages 233-273.
    16. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    17. John William Hatfield & Fuhito Kojima, 2008. "Matching with Contracts: Comment," American Economic Review, American Economic Association, pages 1189-1194.
    18. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, pages 295-328.
    19. John Hatfield & Fuhito Kojima & Yusuke Narita, 2012. "Many-to-Many Matching with Max-Min Preferences," Discussion Papers 12-020, Stanford Institute for Economic Policy Research.
    20. Muriel Niederle & Alvin E. Roth, 2009. "Market Culture: How Rules Governing Exploding Offers Affect Market Performance," American Economic Journal: Microeconomics, American Economic Association, vol. 1(2), pages 199-219, August.
    21. Klaus, Bettina & Walzl, Markus, 2009. "Stable many-to-many matchings with contracts," Journal of Mathematical Economics, Elsevier, vol. 45(7-8), pages 422-434, July.
    22. Yan Chen & Tayfun Sönmez, 2002. "Improving Efficiency of On-Campus Housing: An Experimental Study," American Economic Review, American Economic Association, pages 1669-1686.
    23. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, pages 399-410.
    24. Aytek Erdil & Haluk Ergin, 2007. "What`s the Matter with Tie-breaking? Improving Efficiency in School Choice," Economics Series Working Papers 349, University of Oxford, Department of Economics.
    25. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, pages 197-204.
    26. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, pages 1954-1978.
    27. Kelso, Alexander S, Jr & Crawford, Vincent P, 1982. "Job Matching, Coalition Formation, and Gross Substitutes," Econometrica, Econometric Society, vol. 50(6), pages 1483-1504, November.
    28. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, pages 73-94.
    29. Eric Budish, 2011. "The Combinatorial Assignment Problem: Approximate Competitive Equilibrium from Equal Incomes," Journal of Political Economy, University of Chicago Press, vol. 119(6), pages 1061-1103.
    30. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, pages 233-260.
    31. 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.
    32. Manea, Mihai, 2009. "Asymptotic ordinal inefficiency of random serial dictatorship," Theoretical Economics, Econometric Society.
    33. Ehlers, Lars & Erdil, Aytek, 2010. "Efficient assignment respecting priorities," Journal of Economic Theory, Elsevier, pages 1269-1282.
    34. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, pages 669-689.
    35. John Hatfield, 2009. "Strategy-proof, efficient, and nonbossy quota allocations," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 33(3), pages 505-515, September.
    36. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, pages 608-627.
    37. Roth, Alvin E, 1991. "A Natural Experiment in the Organization of Entry-Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom," American Economic Review, American Economic Association, pages 415-440.
    38. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, pages 1921-1947.
    39. Thomson, William, 1988. "A study of choice correspondences in economies with a variable number of agents," Journal of Economic Theory, Elsevier, pages 237-254.
    40. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, pages 748-780.
    41. Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
    42. Jinpeng Ma, 1996. "On randomized matching mechanisms (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 377-381.
    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. Jörgen Kratz, 2017. "Overlapping multiple object assignments," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 723-753.
    2. Oded Galor & Ömer Özak, 2016. "The Agricultural Origins of Time Preference," American Economic Review, American Economic Association, pages 3064-3103.
    3. Triossi, Matteo & Romero-Medina, Antonio, 2017. "Two-sided strategy-proofness in many-to-many matching markets," UC3M Working papers. Economics 26081, Universidad Carlos III de Madrid. Departamento de Economía.
    4. Mustafa Afacan, 2014. "Fictitious students creation incentives in school choice problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), pages 493-514.
    5. Erlanson, Albin & Flores-Szwagrzak, Karol, 2015. "Strategy-proof assignment of multiple resources," Journal of Economic Theory, Elsevier, pages 137-162.
    6. Triossi, Matteo & Romero Medina, Antonio, 2017. "Group strategy-proof stable mechanisms in priority-based resource allocation under multi-unit demand: a note," UC3M Working papers. Economics 25310, Universidad Carlos III de Madrid. Departamento de Economía.

    More about this item

    Keywords

    Matching; Market design; Stability; Strategy-proofness; Efficiency; Priority; Acyclicity; Essential homogeneity;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • J44 - Labor and Demographic Economics - - Particular Labor Markets - - - Professional Labor Markets and Occupations

    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:eee:gamebe:v:82:y:2013:i:c:p:1-14. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    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 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 profile, as there may be some citations waiting for confirmation.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.