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A Note on Ex-Ante Stable Lotteries

Author

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  • Schlegel, J. C.

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, J. C., 2017. "A Note on Ex-Ante Stable Lotteries," Working Papers 17/06, Department of Economics, City University London.
  • Handle: RePEc:cty:dpaper:17/06
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    File URL: https://openaccess.city.ac.uk/id/eprint/18703/1/Schlegel%20-%20Economics-DP-17_06.pdf
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    References listed on IDEAS

    as
    1. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    2. 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.
    3. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    4. 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.
    5. Kesten, Onur & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    6. Haris Aziz & Bettina Klaus, 2017. "Random Matching under Priorities: Stability and No Envy Concepts," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 17.09, Université de Lausanne, Faculté des HEC, DEEP.
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    Cited by:

    1. 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.
    2. Haris Aziz & Florian Brandl, 2020. "The Vigilant Eating Rule: A General Approach for Probabilistic Economic Design with Constraints," Papers 2008.08991, arXiv.org, revised Oct 2020.

    More about this item

    Keywords

    Matching; School Choice; Lotteries; Ex-Ante Stability;

    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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