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A criterion to compare mechanisms when solutions are not unique, with applications to constrained school choice

Author

Listed:
  • DECERF, Benoit

    (Universit e de Namur)

  • VAN DER LINDEN, Martin

    (Vanderbilt University)

Abstract

We introduce a new criterion to compare the properties of mechanisms when the solution concept used induces multiple solutions. Our criterion generalizes previous approaches in the literature. We use our criterion to compare the stability of constrained versions of the Boston (BOS) and deferred acceptance (DA) school choice mechanisms in which students can only rank a subset of the schools they could potentially access. When students play a Nash equilibrium, we show that there is a stability cost to increasing the number of schools students can rank in DA. On the other hand, when students only play undominated strategies, increasing the number of schools students can rank increases stability. We find sim- ilar results for BOS. We also compare BOS and DA. Whatever the number of schools students can rank, we find that BOS is more stable than DA in Nash equilibrium, but less stable in undominated strategies.

Suggested Citation

  • DECERF, Benoit & VAN DER LINDEN, Martin, 2016. "A criterion to compare mechanisms when solutions are not unique, with applications to constrained school choice," LIDAM Discussion Papers CORE 2016033, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:2016033
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    File URL: https://sites.uclouvain.be/core/publications/coredp/coredp2016.html
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    References listed on IDEAS

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    More about this item

    Keywords

    Multiple solutions; School choice; Stability; Boston mecha- nism; Deferred acceptance mechanism; Nash equilibrium; Undominated strategy;
    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • I20 - Health, Education, and Welfare - - Education - - - General

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