Abstract
We study multistage centralized assignment systems to allocate scarce resources based on priorities in the context of school choice. We characterize schools’ capacity-priority profiles under which an additional stage of assignment may improve student welfare when the deferred acceptance algorithm is used at each stage. If the capacity-priority profile is acyclic, then no student prefers any subgame-perfect Nash equilibrium (SPNE) outcome of the 2-stage system to the truthful dominant-strategy equilibrium outcome of the 1-stage system. If the capacity-priority profile is not acyclic, then an SPNE outcome of the 2-stage system may Pareto dominate the truthful dominant-strategy equilibrium outcome of the 1-stage system. If students are restricted to playing truncation strategies, an additional stage unambiguously improves student welfare: no student prefers the truthful dominant-strategy equilibrium outcome of the 1-stage system to any SPNE outcome of the 2-stage system.
| Original language | English |
|---|---|
| Pages (from-to) | 1145-1173 |
| Number of pages | 29 |
| Journal | Economic Theory |
| Volume | 76 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - 24 Feb 2023 |
Bibliographical note
Funding Information:We thank Lars Ehlers, Guillaume Haeringer, Bettina Klaus, Scott Duke Kominers, Alexey Kushnir, Vikram Manjunath, William Thomson, anonymous referees, and participants at several seminars and conferences for helpful comments. Battal Doğan gratefully acknowledges financial support from the Swiss National Science Foundation (SNSF) and the British Academy/Leverhulme Trust (SRG1819\190133), and the hospitality of the Center of Mathematical Sciences and Applications (CMSA, Harvard University) where part of this paper was written. This paper was circulated as a part of our previous 2017 working paper entitled “How to improve student assignment in Chicago: unified enrollment in school choice,” which is obsolete now.
Publisher Copyright:
© 2023, The Author(s).