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Equivalence of efficiency notions for ordinal assignment problems

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  • Cho, Wonki Jo
  • Doğan, Battal

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.

Suggested Citation

  • Cho, Wonki Jo & Doğan, Battal, 2016. "Equivalence of efficiency notions for ordinal assignment problems," Economics Letters, Elsevier, vol. 146(C), pages 8-12.
    • Handle: RePEc:eee:ecolet:v:146:y:2016:i:c:p:8-12
    DOI: 10.1016/j.econlet.2016.07.007
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    References listed on IDEAS

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    Cited by:

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    More about this item

    Keywords

    Ordinal assignment problem; sd-efficiency; dl-efficiency; ul-efficiency; Ex post efficiency;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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