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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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    1. YIlmaz, Özgür, 2010. "The probabilistic serial mechanism with private endowments," Games and Economic Behavior, Elsevier, vol. 69(2), pages 475-491, July.
    2. Alcalde, Jose, 2013. "Random Housing with Existing Tenants," QM&ET Working Papers 13-5, University of Alicante, D. Quantitative Methods and Economic Theory.
    3. Kojima, Fuhito, 2009. "Random assignment of multiple indivisible objects," Mathematical Social Sciences, Elsevier, vol. 57(1), pages 134-142, January.
    4. Heo, Eun Jeong, 2014. "Probabilistic assignment problem with multi-unit demands: A generalization of the serial rule and its characterization," Journal of Mathematical Economics, Elsevier, vol. 54(C), pages 40-47.
    5. Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-627, June.
    6. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    7. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    8. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    9. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    10. Bogomolnaia, Anna & Heo, Eun Jeong, 2012. "Probabilistic assignment of objects: Characterizing the serial rule," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2072-2082.
    11. Cho, Wonki Jo & Doğan, Battal, 2016. "Equivalence of efficiency notions for ordinal assignment problems," Economics Letters, Elsevier, vol. 146(C), pages 8-12.
    12. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    13. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    14. YIlmaz, Özgür, 2009. "Random assignment under weak preferences," Games and Economic Behavior, Elsevier, vol. 66(1), pages 546-558, May.
    15. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    16. Nehring, Klaus & Puppe, Clemens, 2007. "The structure of strategy-proof social choice -- Part I: General characterization and possibility results on median spaces," Journal of Economic Theory, Elsevier, vol. 135(1), pages 269-305, July.
    17. Alcalde, Jose & Silva-Reus, José Ángel, 2013. "Allocating via Priorities," QM&ET Working Papers 13-3, University of Alicante, D. Quantitative Methods and Economic Theory.
    18. Saban, Daniela & Sethuraman, Jay, 2014. "A note on object allocation under lexicographic preferences," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 283-289.
    19. Eun Heo, 2014. "The extended serial correspondence on a rich preference domain," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 439-454, May.
    20. Kesten, Onur, 2009. "Why do popular mechanisms lack efficiency in random environments?," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2209-2226, September.
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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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