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Equivalence of efficiency notions for ordinal assignment problems

Wonki Cho () and Battal Dogan

Economics Letters, 2016, vol. 146, issue C, 8-12

Abstract: In ordinal (probabilistic) assignment problems, each agent reports his preference rankings over objects and receives a lottery defined over those objects. A common efficiency notion, sd-efficiency, is obtained by extending the preference rankings to preferences over lotteries by means of (first-order) stochastic dominance. Two alternative efficiency notions, which we call dl- and ul-efficiency, are based on downward and upward lexicographic dominance, respectively. We show that sd-, dl-, and ul-efficiency are all equivalent. Noting that the three efficiency notions are a refinement of ex post efficiency—another well-known efficiency notion—we also identify sufficient and necessary conditions on preference profiles under which ex post efficiency is equivalent to the three notions.

Keywords: Ordinal assignment problem; sd-efficiency; dl-efficiency; ul-efficiency; Ex post efficiency (search for similar items in EconPapers)
JEL-codes: C71 C78 D61 D71 (search for similar items in EconPapers)
Date: 2016
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