When Does an Additional Stage Improve Welfare in Centralized Assignment?
34 Pages Posted: 15 Aug 2018 Last revised: 8 Sep 2020
Date Written: September 2, 2020
We study multistage centralized assignments to allocate scarce resources based on priorities in the context of school choice. We characterize the capacity-priority profiles of schools 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 enrollment system to the truthful equilibrium outcome of the 1-stage enrollment system. If the capacity-priority profile is not acyclic, then an SPNE outcome of the 2-stage enrollment system may Pareto dominate the truthful equilibrium outcome of the 1-stage enrollment system.
Keywords: market design, multistage assignment, school choice, deferred acceptance algorithm
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