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The power of randomness in Bayesian optimal mechanism design

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  • Chawla, Shuchi
  • Malec, David
  • Sivan, Balasubramanian

Abstract

We investigate the power of randomness in the context of a fundamental Bayesian optimal mechanism design problem—a single seller aims to maximize expected revenue by allocating multiple kinds of resources to “unit-demand” agents with preferences drawn from a known distribution. When the agents' preferences are single-dimensional Myerson's seminal work (1981) shows that randomness offers no benefit—the optimal mechanism is always deterministic. In the multi-dimensional case, when agents' preferences are arbitrarily correlated, Briest et al. (2010) showed that the gap between the expected revenue obtained by an optimal randomized mechanism and an optimal deterministic mechanism can be unbounded even when a single agent is offered only 4 services. We show that when the agents' values involve no correlation or a specific kind of positive correlation, the benefit of randomness is only a small constant factor.

Suggested Citation

  • Chawla, Shuchi & Malec, David & Sivan, Balasubramanian, 2015. "The power of randomness in Bayesian optimal mechanism design," Games and Economic Behavior, Elsevier, vol. 91(C), pages 297-317.
    • Handle: RePEc:eee:gamebe:v:91:y:2015:i:c:p:297-317
    DOI: 10.1016/j.geb.2012.08.010
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    References listed on IDEAS

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    4. Shuchi Chawla & Jason Hartline & David Malec & Balasubramanian Sivan, 2010. "Sequential Posted Pricing and Multi-parameter Mechanism Design," Discussion Papers 1486, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    5. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
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    9. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
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    Cited by:

    1. Will Ma, 2023. "When Is Assortment Optimization Optimal?," Management Science, INFORMS, vol. 69(4), pages 2088-2105, April.
    2. Yuan Deng & Jieming Mao & Balasubramanian Sivan & Kangning Wang, 2021. "Optimal Pricing Schemes for an Impatient Buyer," Papers 2106.02149, arXiv.org, revised Feb 2023.
    3. Chen, Xi & Diakonikolas, Ilias & Paparas, Dimitris & Sun, Xiaorui & Yannakakis, Mihalis, 2018. "The complexity of optimal multidimensional pricing for a unit-demand buyer," Games and Economic Behavior, Elsevier, vol. 110(C), pages 139-164.
    4. Tim Roughgarden & Inbal Talgam-Cohen & Qiqi Yan, 2019. "Robust Auctions for Revenue via Enhanced Competition," Operations Research, INFORMS, vol. 68(4), pages 1074-1094, July.
    5. Azar, Pablo D. & Kleinberg, Robert & Weinberg, S. Matthew, 2019. "Prior independent mechanisms via prophet inequalities with limited information," Games and Economic Behavior, Elsevier, vol. 118(C), pages 511-532.
    6. Chawla, Shuchi & Teng, Yifeng & Tzamos, Christos, 2022. "Buy-many mechanisms are not much better than item pricing," Games and Economic Behavior, Elsevier, vol. 134(C), pages 104-116.
    7. Moshe Babaioff & Michal Feldman & Yannai A. Gonczarowski & Brendan Lucier & Inbal Talgam-Cohen, 2020. "Escaping Cannibalization? Correlation-Robust Pricing for a Unit-Demand Buyer," Papers 2003.05913, arXiv.org, revised Aug 2020.
    8. Alon Eden & Michal Feldman & Ophir Friedler & Inbal Talgam-Cohen & S. Matthew Weinberg, 2021. "A Simple and Approximately Optimal Mechanism for a Buyer with Complements," Operations Research, INFORMS, vol. 69(1), pages 188-206, January.
    9. Constantinos Daskalakis & Maxwell Fishelson & Brendan Lucier & Vasilis Syrgkanis & Santhoshini Velusamy, 2020. "Multi-item Non-truthful Auctions Achieve Good Revenue," Papers 2002.06702, arXiv.org, revised Sep 2022.
    10. Adam N. Elmachtoub & Michael L. Hamilton, 2021. "The Power of Opaque Products in Pricing," Management Science, INFORMS, vol. 67(8), pages 4686-4702, August.
    11. Kazumura, Tomoya & Mishra, Debasis & Serizawa, Shigehiro, 2020. "Strategy-proof multi-object mechanism design: Ex-post revenue maximization with non-quasilinear preferences," Journal of Economic Theory, Elsevier, vol. 188(C).
    12. Nima Haghpanah & Aditya Kuvalekar & Elliot Lipnowski, 2024. "Buying from a Group," American Economic Review, American Economic Association, vol. 114(8), pages 2596-2632, August.

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    More about this item

    Keywords

    Mechanism design; Randomness; Revenue; Lotteries; Screening; Multi-product pricing;
    All these keywords.

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D44 - Microeconomics - - Market Structure, Pricing, and Design - - - Auctions
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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