When does an additional stage improve welfare in centralized assignment?

Battal Dogan and M. Bumin Yenmez

Economic Theory, 2023, vol. 76, issue 4, No 4, 1145-1173

Abstract: 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.

Keywords: Market design; Multistage assignment; School choice; Deferred acceptance algorithm; C78; D47; D61 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00199-023-01488-y

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