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Strategy-proofness and stability of the Boston mechanism: An almost impossibility result

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  • Kumano, Taro

Abstract

Public school systems generally use one of the three competing mechanisms – the Boston mechanism, the deferred acceptance mechanism and the top trading cycle mechanism – for assigning students to specific schools. Although the literature generally claims that the Boston mechanism is Pareto efficient but neither stable nor strategy-proof, this study delineates a subset of school priority structures for which it fulfills all three criteria. We show that the Boston mechanism is stable if and only if it is strategy-proof if and only if the priority structure is strongly acyclic. However, we find that the condition of strong acyclicity is nearly impossible to satisfy: any priority structure is quasi-cyclic whenever there are two schools whose admission quotas are less than the number of students seeking admission.

Suggested Citation

  • Kumano, Taro, 2013. "Strategy-proofness and stability of the Boston mechanism: An almost impossibility result," Journal of Public Economics, Elsevier, vol. 105(C), pages 23-29.
  • Handle: RePEc:eee:pubeco:v:105:y:2013:i:c:p:23-29 DOI: 10.1016/j.jpubeco.2013.05.008
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    References listed on IDEAS

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    1. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, pages 215-237.
    2. Kojima, Fuhito, 2011. "Robust stability in matching markets," Theoretical Economics, Econometric Society, vol. 6(2), May.
    3. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, pages 1860-1874.
    4. Fuhito Kojima & Mihai Manea, 2010. "Axioms for Deferred Acceptance," Econometrica, Econometric Society, vol. 78(2), pages 633-653, March.
    5. Shapley, Lloyd & Scarf, Herbert, 1974. "On cores and indivisibility," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 23-37, March.
    6. 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.
    7. 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.
    8. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth & Tayfun Sönmez, 2005. "The Boston Public School Match," American Economic Review, American Economic Association, pages 368-371.
    9. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    10. Haluk I. Ergin, 2002. "Efficient Resource Allocation on the Basis of Priorities," Econometrica, Econometric Society, vol. 70(6), pages 2489-2497, November.
    11. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
    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.
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    Cited by:

    1. Paula Jaramillo, 2017. "Minimal consistent enlargements of the immediate acceptance rule and the top trading cycles rule in school choice," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 177-195, January.
    2. repec:spr:reecde:v:21:y:2017:i:2:d:10.1007_s10058-017-0200-1 is not listed on IDEAS
    3. Chen, Yajing, 2014. "When is the Boston mechanism strategy-proof?," Mathematical Social Sciences, Elsevier, vol. 71(C), pages 43-45.
    4. Harless, Patrick, 2014. "A School Choice Compromise: Between Immediate and Deferred Acceptance," MPRA Paper 61417, University Library of Munich, Germany.
    5. Akahoshi, Takashi, 2014. "Singleton core in many-to-one matching problems," Mathematical Social Sciences, Elsevier, vol. 72(C), pages 7-13.
    6. repec:eee:mateco:v:72:y:2017:i:c:p:16-24 is not listed on IDEAS

    More about this item

    Keywords

    Boston mechanism; Stability; Strategy-proofness; Quasi-cyclicity; Strong acyclicity;

    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

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