Efficiency and stability of probabilistic assignments in marriage problems

• 成果类型: Article
• 署名作者: Dogan, Battal; Yildiz, Kemal
• 署名单位: University of Lausanne; Ihsan Dogramaci Bilkent University
• 刊物名称: GAMES AND ECONOMIC BEHAVIOR
• ISSN/ISSBN: 0899-8256
• DOI: 10.1016/j.geb.2015.12.001
• 发表日期: 2016
• 页码: 47-58
• 关键词: Marriage problems; Probabilistic assignment; EFFICIENCY; STABILITY

摘要

We study marriage problems where two groups of agents, men and women, match each other and probabilistic assignments are possible. When only ordinal preferences are observable, stochastic dominance efficiency (sd-efficiency) is commonly used. First, we provide a characterization of sd-efficient allocations in terms of a property of an order relation defined on the set of man-woman pairs. Then, using this characterization, we constructively prove that for each probabilistic assignment that is sd-efficient for some ordinal preferences, there is a von Neumann-Morgenstern utility profile consistent with the ordinal preferences for which the assignment is Pareto efficient. Second, we show that when the preferences are strict, for each ordinal preference profile and each ex post stable probabilistic assignment, there is a von Neumann-Morgenstern utility profile, consistent with the ordinal preferences, for which the assignment belongs to the core of the associated transferable utility game. (C) 2015 Elsevier Inc. All rights reserved.