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Optimal allocation of an indivisible good

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  • Shao, Ran
  • Zhou, Lin

Abstract

In this paper, we consider the problem of allocating an indivisible good efficiently between two agents with monetary transfers. We focus on allocation mechanisms that are dominant-strategy incentive compatible when agents' types are private information. Inefficiency of an allocation mechanism may come from two sources: misallocation of the indivisible good and an imbalanced budget. Unfortunately, as Green and Laffont (1979) demonstrate, no allocation mechanism can always overcome both kinds of inefficiency. We identify allocation mechanisms that maximize the expected total utilities of agents, and characterize optimal mechanisms for a large class of agents' type distributions. For strongly regular type distributions, we show that the optimal mechanisms must be budget-balanced: they are either fixed-price mechanisms or option mechanisms. The result may not hold for other type distributions. For certain type distributions, we show that optimal mechanisms are hybrids of Vickrey–Clarke–Groves mechanisms and budget-balanced mechanisms.

Suggested Citation

  • Shao, Ran & Zhou, Lin, 2016. "Optimal allocation of an indivisible good," Games and Economic Behavior, Elsevier, vol. 100(C), pages 95-112.
    • Handle: RePEc:eee:gamebe:v:100:y:2016:i:c:p:95-112
    DOI: 10.1016/j.geb.2016.09.004
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    2. Conan Mukherjee, 2020. "On group strategyproof and optimal object allocation," Economic Theory Bulletin, Springer;Society for the Advancement of Economic Theory (SAET), vol. 8(2), pages 289-304, October.
    3. Moritz Drexl & Andreas Kleiner, 2018. "Why Voting? A Welfare Analysis," American Economic Journal: Microeconomics, American Economic Association, vol. 10(3), pages 253-271, August.
    4. Kiho Yoon, 2021. "Robust double auction mechanisms," Papers 2102.00669, arXiv.org, revised May 2022.
    5. Long, Yan & Mishra, Debasis & Sharma, Tridib, 2017. "Balanced ranking mechanisms," Games and Economic Behavior, Elsevier, vol. 105(C), pages 9-39.
    6. Blumrosen, Liad & Dobzinski, Shahar, 2021. "(Almost) efficient mechanisms for bilateral trading," Games and Economic Behavior, Elsevier, vol. 130(C), pages 369-383.
    7. Shao, Ran & Zhou, Lin, 2016. "Voting and optimal provision of a public good," Journal of Public Economics, Elsevier, vol. 134(C), pages 35-41.
    8. Kiho Yoon, 2018. "Optimal robust allocation of private goods," Discussion Paper Series 1803, Institute of Economic Research, Korea University.

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    More about this item

    Keywords

    Dominance incentive mechanisms; Average efficiency; Fixed-price mechanisms; Option mechanisms; Budget balance;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D45 - Microeconomics - - Market Structure, Pricing, and Design - - - Rationing; Licensing

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