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When is the probabilistic serial assignment uniquely efficient and envy-free?

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  • Cho, Wonki Jo

Abstract

We study the problem of allocating objects using lotteries. For each economy, the serial assignment, the assignment selected by the (probabilistic) serial rule, is sd-efficient and sd-envy-free (“sd” stands for stochastic dominance) but in general, it is not the only such assignment. Our question is when the uniqueness also holds. First, we provide a necessary condition for uniqueness, termed top-objects divisibility. Exploiting the structure revealed by top-objects divisibility, we then provide two sufficient conditions: preference richness and recursive decomposability. Existing sufficient conditions are restrictive in that they are satisfied only if there are sufficiently many agents relative to the number of objects; and that they only focus on preferences, ignoring other aspects of the problem that are also relevant to uniqueness. Our conditions overcome these limitations and can explain uniqueness for a wide range of economies.

Suggested Citation

  • Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    • Handle: RePEc:eee:mateco:v:66:y:2016:i:c:p:14-25
    DOI: 10.1016/j.jmateco.2016.07.001
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    References listed on IDEAS

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    Cited by:

    1. Liu, Peng, 2020. "Random assignments on sequentially dichotomous domains," Games and Economic Behavior, Elsevier, vol. 121(C), pages 565-584.
    2. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    3. Doğan, Battal & Doğan, Serhat & Yıldız, Kemal, 2018. "A new ex-ante efficiency criterion and implications for the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 175(C), pages 178-200.

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