Browsing by Subject "Probabilistic assignment"

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    Efficiency and stability of probabilistic assignments in marriage problems
    (Academic Press, 2016) Doğan, B.; Yıldız, K.
    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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    A new ex-ante efficiency criterion and implications for the probabilistic serial mechanism
    (Academic Press, 2018) Doğan, B.; Doğan, Serhat; Yıldız, Kemal
    We introduce and analyze an efficiency criterion for probabilistic assignment of objects, when only ordinal preference information is available. This efficiency criterion is based on the following domination relation: a probabilistic assignment dominates another assignment if it is ex-ante efficient for a strictly larger set of utility profiles consistent with the ordinal preferences. We provide a simple characterization of this domination relation. We revisit an extensively studied assignment mechanism, the Probabilistic Serial mechanism (Bogomolnaia and Moulin, 2001), which always chooses a “fair” assignment. We show that the Probabilistic Serial assignment may be dominated by another fair assignment. We provide conditions under which the serial assignment is undominated among fair assignments.