When Does an Additional Stage Improve Welfare in Centralized Assignment?

36 Pages Posted: 15 Aug 2018 Last revised: 7 Feb 2023

See all articles by Battal Doğan

Battal Doğan

School of Economics, University of Bristol

M. Bumin Yenmez

Boston College

Date Written: February 1, 2023

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

Suggested Citation

Doğan, Battal and Yenmez, M. Bumin, When Does an Additional Stage Improve Welfare in Centralized Assignment? (February 1, 2023). Available at SSRN: https://ssrn.com/abstract=3223789 or http://dx.doi.org/10.2139/ssrn.3223789

Battal Doğan (Contact Author)

School of Economics, University of Bristol ( email )

United Kingdom

M. Bumin Yenmez

Boston College ( email )

140 Commonwealth Ave.
Maloney Hall 327
Chestnut Hill, MA 02467
United States

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