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On the constrained efficiency of strategy-proof random assignment

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  • Basteck, Christian
  • Ehlers, Lars H.

Abstract

We study the random assignment of indivisible objects among a set of agents with strict preferences. Random Serial Dictatorship is known to be only ex-post efficient and there exist mechanisms which Pareto-dominate it ex ante. However, we show that there is no mechanism that is likewise (i) strategy-proof and (ii) boundedly invariant, and that Paretodominates Random Serial Dictatorship. Moreover, the same holds for all mechanisms that are ex-post efficient, strategy-proof, and boundedly invariant: no such mechanism is dominated by any other mechanism that is likewise strategy-proof and boundedly invariant.

Suggested Citation

  • Basteck, Christian & Ehlers, Lars H., 2023. "On the constrained efficiency of strategy-proof random assignment," Discussion Papers, Research Unit: Market Behavior SP II 2023-202, WZB Berlin Social Science Center.
    • Handle: RePEc:zbw:wzbmbh:spii2023202
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    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Lars Ehlers, 2002. "Probabilistic allocation rules and single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 19(2), pages 325-348.
    4. Martini, Giorgio, 2016. "Strategy-proof and fair assignment is wasteful," Games and Economic Behavior, Elsevier, vol. 98(C), pages 172-179.
    5. Bogomolnaia, Anna, 2015. "Random assignment: Redefining the serial rule," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 308-318.
    6. Chambers, Christopher P., 2004. "Consistency in the probabilistic assignment model," Journal of Mathematical Economics, Elsevier, vol. 40(8), pages 953-962, December.
    7. 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.
    8. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).
    9. 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.
    10. ,, 2009. "Asymptotic ordinal inefficiency of random serial dictatorship," Theoretical Economics, Econometric Society, vol. 4(2), June.
    11. Priyanka Shende & Manish Purohit, 2020. "Strategy-proof and Envy-free Mechanisms for House Allocation," Papers 2010.16384, arXiv.org.
    12. Zhang, Jun, 2019. "Efficient and fair assignment mechanisms are strongly group manipulable," Journal of Economic Theory, Elsevier, vol. 180(C), pages 167-177.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    random assignment; strategy-proofness; ex-post efficiency; bounded invariance;
    All these keywords.

    JEL classification:

    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General

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