Best-Response Dynamics in the Boston Mechanism

Abstract

I analyze a setting where the Boston Mechanism (BM) is applied repeatedly and students form their application strategies by best-responding to the admission cutoffs of the previous period, a process I call the Repeated Boston Mechanism (RBM). If students are truthful in the initial period, the allocation under RBM converges in finite time to the student optimal stable matching (SOSM), which is the Pareto-dominant equilibrium of BM and the outcome of the strategy-proof Deferred Acceptance Mechanism. If some students are sincere and do not strategize, then the allocation under RBM with sincere students converges to the SOSM of a market in which sincere students lose their priorities. When students best-reply to some initial cutoffs in the first period, RBM converges to SOSM if students are initially optimistic about their admissions chances but may cycle between allocations Pareto-dominated by SOSM if they are pessimistic. My results provide a foundation for equilibrium analysis under BM and help explain why students play suboptimal and overcautious strategies.

Keywords: Matching Theory, Market Design, Boston Mechanism, Best-Response Dynamics

JEL Classification: C78, D47