Efficiency and stability of probabilistic assignments in marriage problems

Date
2016
Authors
Doğan, B.
Yıldız, K.
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Source Title
Games and Economic Behavior
Print ISSN
0899-8256
Electronic ISSN
1090-2473
Publisher
Academic Press
Volume
95
Issue
Pages
47 - 58
Language
English
Type
Article
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Abstract

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. © 2015 Elsevier Inc.

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Keywords
Efficiency, Marriage problems, Probabilistic assignment, Stability
Citation
Published Version (Please cite this version)