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Crowding in School Choice

Author

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  • William PHAN
  • Ryan TIERNEY
  • Yu ZHOU

Abstract

We consider the problem of matching students to schools when students are able to express preferences over crowding. For example, schools have varying per capita expenditures, average teacherstudent ratios, etc. These characteristics of a school are now endogenously determined—matchings with more students to a particular school decrease each of the variables above. We propose a new equilibrium notion, the Rationing Crowding Equilibrium (RCE), that accommodates crowding, noenvy, and respect for priorities. We prove the existence of RCE under mild domain conditions, and establish a Rural Hospitals Theorem and welfare lattice result on the set of RCE. The latter implies the existence of a maximal RCE, and that such RCE are studentoptimal. Moreover, the mechanism defined by selection from the maximal RCE correspondence is strategyproof. We also identify an algorithm to find a maximal RCE for a natural subdomain.

Suggested Citation

  • William PHAN & Ryan TIERNEY & Yu ZHOU, 2021. "Crowding in School Choice," Discussion papers e-21-006, Graduate School of Economics , Kyoto University.
    • Handle: RePEc:kue:epaper:e-21-006
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    References listed on IDEAS

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    1. Dur, Umut & Morrill, Thayer, 2018. "Competitive equilibria in school assignment," Games and Economic Behavior, Elsevier, vol. 108(C), pages 269-274.
    2. Tierney, Ryan, 2019. "The problem of multiple commons: A market design approach," Games and Economic Behavior, Elsevier, vol. 114(C), pages 1-27.
    3. Echenique, Federico & Yenmez, M. Bumin, 2007. "A solution to matching with preferences over colleagues," Games and Economic Behavior, Elsevier, vol. 59(1), pages 46-71, April.
    4. Talman, Dolf & Yang, Zaifu, 2008. "A dynamic auction for differentiated items under price rigidities," Economics Letters, Elsevier, vol. 99(2), pages 278-281, May.
    5. Dur, Umut Mert & Wiseman, Thomas, 2019. "School choice with neighbors," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 101-109.
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    Cited by:

    1. Tomoya KAZUMURA, 2020. "When can we design efficient and strategy-proof rules in package assignment problems?," Discussion papers e-21-008, Graduate School of Economics , Kyoto University.

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    More about this item

    Keywords

    School choice with crowding; Rationing crowding equilibrium; Student optimality;Strategyproofness;

    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
    • D62 - Microeconomics - - Welfare Economics - - - Externalities
    • I20 - Health, Education, and Welfare - - Education - - - General

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