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

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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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