IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/41366.html
   My bibliography  Save this paper

A Characterization of the Top Trading Cycles Mechanism for the School Choice Problem

Author

Listed:
  • Dur, Umut

Abstract

This paper characterizes the top trading cycles mechanism for the school choice problem. Schools may have multiple available seats to be assigned to students. For each school a strict priority ordering of students is determined by the school district. Each student has strict preference over the schools. We first define weaker forms of fairness, consistency and resource monotonicity. We show that the top trading cycles mechanism is the unique Pareto efficient and strategy-proof mechanism that satisfies the weaker forms of fairness, consistency and resource monotonicity. To our knowledge this is the first axiomatic approach to the top trading cycles mechanism in the school choice problem where schools have a capacity greater than one.

Suggested Citation

  • Dur, Umut, 2012. "A Characterization of the Top Trading Cycles Mechanism for the School Choice Problem," MPRA Paper 41366, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41366
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/41366/1/MPRA_paper_41366.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Lars Ehlers & Bettina Klaus, 2003. "Resource-Monotonicity for House Allocation," Working Papers 33, Barcelona School of Economics.
    2. Alcalde, Jose & Barbera, Salvador, 1994. "Top Dominance and the Possibility of Strategy-Proof Stable Solutions to Matching Problems," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 4(3), pages 417-435, May.
    3. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
    4. Lars Ehlers & Bettina Klaus, 2004. "Resource-monotonicity for house allocation problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 545-560, August.
    5. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    6. Parag A. Pathak, 2011. "The Mechanism Design Approach to Student Assignment," Annual Review of Economics, Annual Reviews, vol. 3(1), pages 513-536, September.
    7. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    8. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    9. Ergin, Haluk I., 2000. "Consistency in house allocation problems," Journal of Mathematical Economics, Elsevier, vol. 34(1), pages 77-97, August.
    10. Chun, Youngsub & Thomson, William, 1988. "Monotonicity properties of bargaining solutions when applied to economics," Mathematical Social Sciences, Elsevier, vol. 15(1), pages 11-27, February.
    11. 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)

    Citations

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


    Cited by:

    1. Atila Abdulkadiroglu & Yeon-Koo Che & Parag A. Pathak & Alvin E. Roth & Olivier Tercieux, 2017. "Minimizing Justified Envy in School Choice: The Design of New Orleans' OneApp," NBER Working Papers 23265, National Bureau of Economic Research, Inc.
    2. Patrick Harless & William Phan, 2020. "On endowments and indivisibility: partial ownership in the Shapley–Scarf model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(2), pages 411-435, September.
    3. Dur, Umut Mert, 2019. "The modified Boston mechanism," Mathematical Social Sciences, Elsevier, vol. 101(C), pages 31-40.
    4. Umut Mert Dur & M. Utku Unver, 2015. "Two-Sided Matching via Balanced Exchange: Tuition and Worker Exchanges," Koç University-TUSIAD Economic Research Forum Working Papers 1508, Koc University-TUSIAD Economic Research Forum.
    5. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
    6. Dur, Umut Mert & Wiseman, Thomas, 2019. "School choice with neighbors," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 101-109.
    7. 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.
    8. Nadja Stroh-Maraun, 2020. "Pareto Efficiency in Weighted School Choice Problems," Working Papers Dissertations 64, Paderborn University, Faculty of Business Administration and Economics.
    9. Siwei Chen & Yajing Chen & Chia‐Ling Hsu, 2023. "New axioms for top trading cycles," Bulletin of Economic Research, Wiley Blackwell, vol. 75(4), pages 1064-1077, October.
    10. Martin Bichler & Alexander Hammerl & Thayer Morrill & Stefan Waldherr, 2021. "How to Assign Scarce Resources Without Money: Designing Information Systems that are Efficient, Truthful, and (Pretty) Fair," Information Systems Research, INFORMS, vol. 32(2), pages 335-355, June.
    11. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
    12. Afacan, Mustafa Oǧuz, 2013. "Alternative characterizations of Boston mechanism," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 176-179.

    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. 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.
    2. 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.
    3. 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.
    4. Ehlers, Lars & Klaus, Bettina, 2006. "Efficient priority rules," Games and Economic Behavior, Elsevier, vol. 55(2), pages 372-384, May.
    5. John William Hatfield & Fuhito Kojima & Yusuke Narita, 2011. "Promoting School Competition Through School Choice: A Market Design Approach," Working Papers 2011-018, Human Capital and Economic Opportunity Working Group.
    6. Han, Xiang, 2018. "Stable and efficient resource allocation under weak priorities," Games and Economic Behavior, Elsevier, vol. 107(C), pages 1-20.
    7. Benedict Dellaert & Vladislav Golounov & Jaideep Prabhu, 2005. "The Impact of Price Disclosure on Dynamic Shopping Decisions," Marketing Letters, Springer, vol. 16(1), pages 37-52, January.
    8. Bettina Klaus & Flip Klijn, 2007. "Fair and efficient student placement with couples," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(2), pages 177-207, October.
    9. Rustamdjan Hakimov & Onur Kesten, 2018. "The Equitable Top Trading Cycles Mechanism For School Choice," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 59(4), pages 2219-2258, November.
    10. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
    11. Schummer, James & Abizada, Azar, 2017. "Incentives in landing slot problems," Journal of Economic Theory, Elsevier, vol. 170(C), pages 29-55.
    12. Kesten, Onur, 2006. "On two competing mechanisms for priority-based allocation problems," Journal of Economic Theory, Elsevier, vol. 127(1), pages 155-171, March.
    13. Sonmez, Tayfun & Utku Unver, M., 2005. "House allocation with existing tenants: an equivalence," Games and Economic Behavior, Elsevier, vol. 52(1), pages 153-185, July.
    14. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    15. Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
    16. Karakaya, Mehmet & Klaus, Bettina & Schlegel, Jan Christoph, 2019. "Top trading cycles, consistency, and acyclic priorities for house allocation with existing tenants," Journal of Economic Theory, Elsevier, vol. 184(C).
    17. Klaus, Bettina & Klijn, Flip, 2013. "Local and global consistency properties for student placement," Journal of Mathematical Economics, Elsevier, vol. 49(3), pages 222-229.
    18. Kesten, Onur & Kurino, Morimitsu, 2019. "Strategy-proof improvements upon deferred acceptance: A maximal domain for possibility," Games and Economic Behavior, Elsevier, vol. 117(C), pages 120-143.
    19. Pablo Guillen & Onur Kesten, 2012. "Matching Markets With Mixed Ownership: The Case For A Real‐Life Assignment Mechanism," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(3), pages 1027-1046, August.
    20. Anno, Hidekazu & Kurino, Morimitsu, 2016. "On the operation of multiple matching markets," Games and Economic Behavior, Elsevier, vol. 100(C), pages 166-185.

    More about this item

    Keywords

    Top Trading Cycles Mechanism; School Choice Problem;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • I20 - Health, Education, and Welfare - - Education - - - General
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:pra:mprapa:41366. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.