A Criterion to Compare Mechanisms When Solutions Are Not Unique, with Applications to Constrained School Choice

36 Pages Posted: 17 Jul 2016

See all articles by Benoit Decerf

Benoit Decerf

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Martin Van der Linden

Emory University

Date Written: July 14, 2016

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 similar 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.

Keywords: Multiple solutions, School choice, Stability, Boston mechanism, Deferred acceptance mechanism, Nash equilibrium, Undominated strategy

JEL Classification: C78, D47, D82, I20

Suggested Citation

Decerf, Benoit and Van der Linden, Martin, A Criterion to Compare Mechanisms When Solutions Are Not Unique, with Applications to Constrained School Choice (July 14, 2016). Available at SSRN: https://ssrn.com/abstract=2809570 or http://dx.doi.org/10.2139/ssrn.2809570

Benoit Decerf

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Martin Van der Linden (Contact Author)

Emory University ( email )

201 Dowman Drive
Atlanta, GA 30322
United States

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