Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5057981 | Economics Letters | 2016 | 5 Pages |
â¢We study four efficiency notions in ordinal assignment problems.â¢We show that sd-, dl-, and ul-efficiency are equivalent.â¢We provide conditions for equivalence of the three notions and ex post efficiency.â¢Our conditions are sufficient and necessary for the equivalence.
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.