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

• 成果类型: Article
• 署名作者: Bando, Keisuke
• 署名单位: Institute of Science Tokyo; Tokyo Institute of Technology
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2014.05.009
• 发表日期: 2014
• 页码: 269-287
• 关键词: Student-optimal deferred acceptance algorithm; Strictly strong Nash equilibrium; Efficiency-adjusted deferred acceptance algorithm; Student-optimal vNM stable matching

摘要

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. (C) 2014 Elsevier Inc. All rights reserved.