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School choice with preference rank classes

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  • Ayoade, Nickesha
  • Pápai, Szilvia

Abstract

We introduce and study a large family of rules for many-to-one matching problems, the Preference Rank Partitioned (PRP) rules. PRP rules are student-proposing Deferred Acceptance rules, where the schools select among applicants in each round taking into account both the students' preferences and the schools' priorities. In a PRP rule each school first seeks to select students based on priority rank classes, and subsequently based on preference rank classes. PRP rules include many well-known matching rules, such as the classic Deferred Acceptance rule, the Boston rule, the Chinese Application-Rejection rules of Chen and Kesten (2017), and the French Priority rules of Bonkoungou (2020), in addition to matching rules that have not been studied yet. We analyze the stability, efficiency and incentive properties of PRP rules in this unified framework.

Suggested Citation

  • Ayoade, Nickesha & Pápai, Szilvia, 2023. "School choice with preference rank classes," Games and Economic Behavior, Elsevier, vol. 137(C), pages 317-341.
    • Handle: RePEc:eee:gamebe:v:137:y:2023:i:c:p:317-341
    DOI: 10.1016/j.geb.2022.11.011
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    1. Ehlers, Lars & Hafalir, Isa E. & Yenmez, M. Bumin & Yildirim, Muhammed A., 2014. "School choice with controlled choice constraints: Hard bounds versus soft bounds," Journal of Economic Theory, Elsevier, vol. 153(C), pages 648-683.
    2. Ehlers, Lars & Westkamp, Alexander, 2018. "Strategy-proof tie-breaking in matching with priorities," Theoretical Economics, Econometric Society, vol. 13(3), September.
    3. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January.
    4. Parag A. Pathak & Tayfun Sonmez, 2008. "Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism," American Economic Review, American Economic Association, vol. 98(4), pages 1636-1652, September.
    5. Ehlers, Lars & Klaus, Bettina, 2016. "Object allocation via deferred-acceptance: Strategy-proofness and comparative statics," Games and Economic Behavior, Elsevier, vol. 97(C), pages 128-146.
    6. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    7. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-proofness versus Efficiency in Matching with Indifferences: Redesigning the New York City High School Match," NBER Working Papers 14864, National Bureau of Economic Research, Inc.
    8. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    9. Doğan, Battal & Klaus, Bettina, 2018. "Object allocation via immediate-acceptance: Characterizations and an affirmative action application," Journal of Mathematical Economics, Elsevier, vol. 79(C), pages 140-156.
    10. Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-427, March.
    11. 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.
    12. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, vol. 101(1), pages 399-410, February.
    13. 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.
    14. 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.
    15. 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.
    16. Bonkoungou, Somouaoga & Nesterov, Alexander, 2021. "Comparing school choice and college admissions mechanisms by their strategic accessibility," Theoretical Economics, Econometric Society, vol. 16(3), July.
    17. Ehlers, Lars & Erdil, Aytek, 2010. "Efficient assignment respecting priorities," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1269-1282, May.
    18. 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.
    19. , Emin & , Bumin & , Ali, 2013. "Effective affirmative action in school choice," Theoretical Economics, Econometric Society, vol. 8(2), May.
    20. 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, vol. 81(3), pages 415-440, June.
    21. Hirata, Daisuke & Kasuya, Yusuke, 2017. "On stable and strategy-proof rules in matching markets with contracts," Journal of Economic Theory, Elsevier, vol. 168(C), pages 27-43.
    22. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    23. Troyan, Peter & Morrill, Thayer, 2020. "Obvious manipulations," Journal of Economic Theory, Elsevier, vol. 185(C).
    24. Umut Dur & Robert G. Hammond & Thayer Morrill, 2019. "The Secure Boston Mechanism: theory and experiments," Experimental Economics, Springer;Economic Science Association, vol. 22(4), pages 918-953, December.
    25. Dilek Sayedahmed, 2022. "Centralized refugee matching mechanisms with hierarchical priority classes," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 7(1), pages 71-111, December.
    26. Mark A. Satterthwaite & Hugo Sonnenschein, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 587-597.
    27. Afacan, Mustafa Oǧuz, 2013. "Alternative characterizations of Boston mechanism," Mathematical Social Sciences, Elsevier, vol. 66(2), pages 176-179.
    28. Chen, Yan & Kesten, Onur, 2019. "Chinese college admissions and school choice reforms: An experimental study," Games and Economic Behavior, Elsevier, vol. 115(C), pages 83-100.
    29. 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, vol. 99(5), pages 1954-1978, December.
    30. Umut Dur & Parag A. Pathak & Fei Song & Tayfun Sönmez, 2022. "Deduction Dilemmas: The Taiwan Assignment Mechanism," American Economic Journal: Microeconomics, American Economic Association, vol. 14(1), pages 164-185, February.
    31. Peter Chen & Michael Egesdal & Marek Pycia & M. Bumin Yenmez, 2016. "Manipulability of Stable Mechanisms," American Economic Journal: Microeconomics, American Economic Association, vol. 8(2), pages 202-214, May.
    32. Alva, Samson & Manjunath, Vikram, 2019. "Strategy-proof Pareto-improvement," Journal of Economic Theory, Elsevier, vol. 181(C), pages 121-142.
    33. Kamada, Yuichiro & Kojima, Fuhito, 2018. "Stability and strategy-proofness for matching with constraints: a necessary and sufficient condition," Theoretical Economics, Econometric Society, vol. 13(2), May.
    34. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    35. Alvin E. Roth, 1982. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, INFORMS, vol. 7(4), pages 617-628, November.
    36. Yan Chen & Onur Kesten, 2017. "Chinese College Admissions and School Choice Reforms: A Theoretical Analysis," Journal of Political Economy, University of Chicago Press, vol. 125(1), pages 99-139.
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    More about this item

    Keywords

    Matching; School choice; Deferred Acceptance; Boston rule; Stability; Efficiency; Manipulation;
    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
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation

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