IDEAS home Printed from https://ideas.repec.org/p/pdn/dispap/64.html
   My bibliography  Save this paper

Pareto Efficiency in Weighted School Choice Problems

Author

Listed:
  • Nadja Stroh-Maraun

    (Paderborn University)

Abstract

There are a number of school choice problems in which students are heterogeneous according to the number of seats they occupy at the school they are assigned to. We propose a weighted school choice problem by assigning each student a so-called weight and extend the top trading cycles algorithm to fit to this extension. We call the new mechanism the weighted TTC and show that it is strategy-proof and results in a Pareto efficient matching. Therefore, the TTC is robust towards the introduction of weights. Nevertheless, it is more complex to guarantee each student a seat at a school, as the extension introduces a trade-off between weights and priorities.

Suggested Citation

  • Nadja Stroh-Maraun, 2020. "Pareto Efficiency in Weighted School Choice Problems," Working Papers Dissertations 64, Paderborn University, Faculty of Business Administration and Economics.
    • Handle: RePEc:pdn:dispap:64
    as

    Download full text from publisher

    File URL: http://groups.uni-paderborn.de/wp-wiwi/RePEc/pdf/dispap/DP64.pdf
    Download Restriction: no
    ---><---

    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, vol. 100(4), pages 1860-1874, September.
    2. 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.
    3. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    4. Dur, Umut Mert & Wiseman, Thomas, 2019. "School choice with neighbors," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 101-109.
    5. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    6. Carlsson, Sissa & Thomsen, Stephan L., 2015. "Improving the Allocation of Spots in Child Care Facilities for Toddlers in Germany: A Mechanism Design Approach," IZA Discussion Papers 8976, Institute of Labor Economics (IZA).
    7. Ashlagi, Itai & Gonczarowski, Yannai A., 2018. "Stable matching mechanisms are not obviously strategy-proof," Journal of Economic Theory, Elsevier, vol. 177(C), pages 405-425.
    8. James J. Heckman & Dimitriy V. Masterov, 2007. "The Productivity Argument for Investing in Young Children ," Review of Agricultural Economics, Agricultural and Applied Economics Association, vol. 29(3), pages 446-493.
    9. Dur, Umut & Paiement, Scott, 2024. "A characterization of the top trading cycles mechanism for the school choice problem," Mathematical Social Sciences, Elsevier, vol. 129(C), pages 93-100.
    10. Chen, Yan & Sonmez, Tayfun, 2006. "School choice: an experimental study," Journal of Economic Theory, Elsevier, vol. 127(1), pages 202-231, March.
    11. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
    12. Shengwu Li, 2017. "Obviously Strategy-Proof Mechanisms," American Economic Review, American Economic Association, vol. 107(11), pages 3257-3287, November.
    13. 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.
    14. Yan Chen & Yingzhi Liang & Tayfun Sönmez, 2016. "School choice under complete information: An experimental study," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 1(1), pages 45-82, December.
    15. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    16. Thayer Morrill, 2013. "An alternative characterization of top trading cycles," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 181-197, September.
    17. 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.
    18. Aytek Erdil & Haluk Ergin, 2008. "What's the Matter with Tie-Breaking? Improving Efficiency in School Choice," American Economic Review, American Economic Association, vol. 98(3), pages 669-689, June.
    19. A. Chevalier & T. K. Viitanen, 2002. "The causality between female labour force participation and the availability of childcare," Applied Economics Letters, Taylor & Francis Journals, vol. 9(14), pages 915-918.
    20. Haake, Claus-Jochen & Stroh-Maraun, Nadja, 2018. "Outcome equivalence in school choice with reciprocal preferences," Economics Letters, Elsevier, vol. 170(C), pages 39-41.
    21. Hoyer, B. & Stroh-Maraun, N., 2020. "Matching strategies of heterogeneous agents under incomplete information in a university clearinghouse," Games and Economic Behavior, Elsevier, vol. 121(C), pages 453-481.
    22. Roth, Alvin E. & Postlewaite, Andrew, 1977. "Weak versus strong domination in a market with indivisible goods," Journal of Mathematical Economics, Elsevier, vol. 4(2), pages 131-137, August.
    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. Abdulkadiroglu, Atila & Andersson, Tommy, 2022. "School Choice," Working Papers 2022:4, Lund University, Department of Economics.
    2. Biró, Péter & Gudmundsson, Jens, 2021. "Complexity of finding Pareto-efficient allocations of highest welfare," European Journal of Operational Research, Elsevier, vol. 291(2), pages 614-628.
    3. 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.
    4. Pablo Guillen & Róbert F. Veszteg, 2021. "Strategy-proofness in experimental matching markets," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 650-668, June.
    5. Morrill, Thayer & Roth, Alvin E., 2024. "Top trading cycles," Journal of Mathematical Economics, Elsevier, vol. 112(C).
    6. 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.
    7. Britta Hoyer & Nadja Stroh-Maraun, 2020. "Stability in Weighted College Admissions Problems," Working Papers Dissertations 63, Paderborn University, Faculty of Business Administration and Economics.
    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. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    10. Min Zhu, 2013. "College Admissions in China : A Mechanism Design Perspective," Working Papers 1327, Groupe d'Analyse et de Théorie Economique Lyon St-Étienne (GATE Lyon St-Étienne), Université de Lyon.
    11. Zhu, Min, 2014. "College admissions in China: A mechanism design perspective," China Economic Review, Elsevier, vol. 30(C), pages 618-631.
    12. Committee, Nobel Prize, 2012. "Alvin E. Roth and Lloyd S. Shapley: Stable allocations and the practice of market design," Nobel Prize in Economics documents 2012-1, Nobel Prize Committee.
    13. Rustamdjan Hakimov & Dorothea Kübler, 2021. "Experiments on centralized school choice and college admissions: a survey," Experimental Economics, Springer;Economic Science Association, vol. 24(2), pages 434-488, June.
    14. Afacan, Mustafa Oğuz & Hu, Gaoji & Li, Jiangtao, 2024. "Housing markets since Shapley and Scarf," Journal of Mathematical Economics, Elsevier, vol. 111(C).
    15. Pinaki Mandal, 2022. "Simple dominance of fixed priority top trading cycles," Papers 2204.02154, arXiv.org, revised Feb 2023.
    16. Zhang, Jun, 2021. "Level-k reasoning in school choice," Games and Economic Behavior, Elsevier, vol. 128(C), pages 1-17.
    17. Jingsheng Yu & Jun Zhang, 2020. "Efficient and fair trading algorithms in market design environments," Papers 2005.06878, arXiv.org, revised May 2021.
    18. Avinatan Hassidim & Assaf Romm & Ran I. Shorrer, 2021. "The Limits of Incentives in Economic Matching Procedures," Management Science, INFORMS, vol. 67(2), pages 951-963, February.
    19. 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, vol. 103(1), pages 80-106, February.
    20. Fuhito Kojima & M. Utku Ünver, 2010. "The 'Boston' School-Choice Mechanism," Boston College Working Papers in Economics 729, Boston College Department of Economics, revised 08 Oct 2010.

    More about this item

    Keywords

    Matching; School Choice; College Admission Problems; Top Trading Cycles; Pareto Efficiency; Strategy-Proofness;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

    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:pdn:dispap:64. 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: WP-WiWi-Info (email available below). General contact details of provider: https://edirc.repec.org/data/fwpadde.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.