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

Benoît Decerf () and Martin Van der Linden

No 2016033, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

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.

Keywords: Multiple solutions; School choice; Stability; Boston mecha- nism; Deferred acceptance mechanism; Nash equilibrium; Undominated strategy (search for similar items in EconPapers)
JEL-codes: C78 D47 D82 I20 (search for similar items in EconPapers)
Date: 2016-10-04
New Economics Papers: this item is included in nep-edu, nep-gth, nep-mic and nep-ure
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