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Ex-Ante Stable Lotteries

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  • Jan Christoph Schlegel

Abstract

We study the allocation of indivisible objects (e.g. school seats) to agents by lotteries. Agents have preferences over different objects and have different priorities at different objects. The priorities can contain indifferences, some agents may have the same priority at some object. A lottery is ex-ante stable if there does not exist an agent-object pair such that we can increase the probability of matching this pair at the expense of agents, who have lower priority at the object, and of objects which are less preferred by the agent. As a first result, we show that this fairness condition is very demanding: Only few agent-object pairs have a positive probability of being matched. The number of pairs in the support depends on how many indifferences in the priorities the lottery exploits. In the extreme case where no object is matched with positive probability to two equal priority agents, the lottery is almost degenerate. Otherwise, the size of the support is completely determined by the size of the lowest priority classes of which agents are matched to the respective objects. 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. As a second result, we derive a new characterization of the set of lotteries that can be decentralized by a pseudo-market with priority-specific pricing as introduced by He et al. (2015). These allocations coincide with the ex-ante stable lotteries that do not admit a strong stable improvement cycle.

Suggested Citation

  • Jan Christoph Schlegel, 2016. "Ex-Ante Stable Lotteries," Cahiers de Recherches Economiques du Département d'Econométrie et d'Economie politique (DEEP) 16.23, Université de Lausanne, Faculté des HEC, DEEP.
  • Handle: RePEc:lau:crdeep:16.23
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    File URL: http://hec.unil.ch/attachments/deep/series/2016/16.23.pdf
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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 & Ünver, M. Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    3. Federico Echenique & Sangmok Lee & Matthew Shum & M. Bumin Yenmez, 2013. "The Revealed Preference Theory of Stable and Extremal Stable Matchings," Econometrica, Econometric Society, vol. 81(1), pages 153-171, January.
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    Cited by:

    1. 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.

    More about this item

    Keywords

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

    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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