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A note on ex-ante stable lotteries

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  • Schlegel, Jan Christoph

Abstract

We study ex-ante priority respecting (ex-ante stable) lotteries in the context of object allocation under thick priorities. We show that ex-ante stability as a fairness condition is very demanding: Only few agent–object pairs have a positive probability of being matched in an ex-ante stable assignment. We interpret our result as an impossibility result. With ex-ante stability, one cannot go much beyond randomly breaking ties and implementing a (deterministically) stable matching with respect to the broken ties.

Suggested Citation

  • Schlegel, Jan Christoph, 2018. "A note on ex-ante stable lotteries," Economics Letters, Elsevier, vol. 164(C), pages 90-93.
    • Handle: RePEc:eee:ecolet:v:164:y:2018:i:c:p:90-93
    DOI: 10.1016/j.econlet.2018.01.017
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    References listed on IDEAS

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    1. Yinghua He & Antonio Miralles & Marek Pycia & Jianye Yan, 2018. "A Pseudo-Market Approach to Allocation with Priorities," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 272-314, August.
    2. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    3. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    4. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    5. Alvin E. Roth & Uriel G. Rothblum & John H. Vande Vate, 1993. "Stable Matchings, Optimal Assignments, and Linear Programming," Mathematics of Operations Research, INFORMS, vol. 18(4), pages 803-828, November.
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    Citations

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    Cited by:

    1. Schlegel, Jan Christoph & Mamageishvili, Akaki, 2020. "Welfare theorems for random assignments with priorities," Games and Economic Behavior, Elsevier, vol. 124(C), pages 62-81.
    2. Neme, Pablo & Oviedo, Jorge, 2021. "On the set of many-to-one strongly stable fractional matchings," Mathematical Social Sciences, Elsevier, vol. 110(C), pages 1-13.
    3. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Jul 2021.
    4. Haris Aziz & Bettina Klaus, 2019. "Random matching under priorities: stability and no envy concepts," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(2), pages 213-259, August.

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    More about this item

    Keywords

    Matching; School choice; Lotteries; Ex-ante stability;
    All these keywords.

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design

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