Efficiency and Stability of Probabilistic Assignments in Marriage Problems

27 Pages Posted: 20 Jul 2014 Last revised: 30 Oct 2015

See all articles by Battal Dogan

Battal Dogan

Department of Economics, University of Bristol

Kemal Yildiz

Bilkent University - Department of Economics

Date Written: October 29, 2015

Abstract

We study marriage problems where two groups of agents match to each other and probabilistic assignments are possible. When only ordinal preferences are observable, an extensively studied efficiency notion is stochastic dominance efficiency (sd-efficiency). 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. Next, we analyze stability of probabilistic assignments. We show that, when the preferences are strict, for each probabilistic assignment that is ex-post stable for some ordinal preferences, there is a von Neumann-Morgenstern utility profile consistent with the ordinal preferences such that the assignment belongs to the core: no coalition can deviate to another probabilistic assignment among themselves and achieve a higher total expected utility.

Keywords: Marriage problems, probabilistic assignment, efficiency, stability

JEL Classification: C60, C71, C78, D61

Suggested Citation

Dogan, Battal and Yildiz, Kemal, Efficiency and Stability of Probabilistic Assignments in Marriage Problems (October 29, 2015). Available at SSRN: https://ssrn.com/abstract=2468339 or http://dx.doi.org/10.2139/ssrn.2468339

Battal Dogan

Department of Economics, University of Bristol ( email )

United Kingdom

Kemal Yildiz (Contact Author)

Bilkent University - Department of Economics ( email )

Bilkent University, Dept. of Economics
BILKENT
Ankara, 06800
Turkey

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