On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm

Keisuke Bando

Research output: Contribution to journalArticlepeer-review

10 Citations (Scopus)

Abstract

This study analyzes a preference revelation game in the student-optimal deferred acceptance algorithm in a college admission problem. We assume that each college's true preferences are known publicly, and analyze the strategic behavior of students. We demonstrate the existence of a strictly strong Nash equilibrium in the preference revelation game through a simple algorithm that finds it. Specifically, (i) the equilibrium outcome from our algorithm is the same matching as in the efficiency-adjusted deferred acceptance algorithm and (ii) in a one-to-one matching market, it coincides with the student-optimal von Neumann-Morgenstern (vNM) stable matching. We also show that (i) when a strict core allocation in a housing market derived from a college admission market exists, it can be supported by a strictly strong Nash equilibrium, and (ii) there exists a strictly strong Nash equilibrium under the college-optimal deferred acceptance algorithm if and only if the student-optimal stable matching is Pareto-efficient for students.

Original languageEnglish
Pages (from-to)269-287
Number of pages19
JournalGames and Economic Behavior
Volume87
DOIs
Publication statusPublished - 2014 Sep
Externally publishedYes

Keywords

  • Efficiency-adjusted deferred acceptance algorithm
  • Strictly strong Nash equilibrium
  • Student-optimal deferred acceptance algorithm
  • Student-optimal vNM stable matching

ASJC Scopus subject areas

  • Finance
  • Economics and Econometrics

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