Equivalence of Efficiency Notions for Ordinal Assignment Problems
10 Pages Posted: 24 Apr 2016
Date Written: April 21, 2016
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
JEL Classification: C71, C78, D61, D71
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