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How Good Are Simple Mechanisms for Selling Multiple Goods?

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  • Sergiu Hart
  • Noam Nisan

Abstract

Maximizing the revenue from selling two goods (or items) is a notoriously difficult problem, in stark contrast to the single-good case. We show that simple "one-dimensional" mechanisms, such as selling the two goods separately, guarantee at least 73% of the optimal revenue when the valuations of the two goods are independent and identically distributed, and at least 50% when they are independent. However, in the general case where the valuations may be correlated, simple mechanisms cannot guarantee any positive fraction of the optimal revenue. We also introduce a "measure of complexity" for mechanisms---the menu size---and show that it is naturally related to the fraction of the optimal revenue that can be guaranteed.

Suggested Citation

  • Sergiu Hart & Noam Nisan, 2014. "How Good Are Simple Mechanisms for Selling Multiple Goods?," Discussion Paper Series dp666, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
    • Handle: RePEc:huj:dispap:dp666
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    Cited by:

    1. , & , J., 2015. "Maximal revenue with multiple goods: nonmonotonicity and other observations," Theoretical Economics, Econometric Society, vol. 10(3), September.
    2. Ningyuan Chen & Adam N. Elmachtoub & Michael L. Hamilton & Xiao Lei, 2021. "Loot Box Pricing and Design," Management Science, INFORMS, vol. 67(8), pages 4809-4825, August.
    3. Menicucci, Domenico & Hurkens, Sjaak & Jeon, Doh-Shin, 2015. "On the optimality of pure bundling for a monopolist," Journal of Mathematical Economics, Elsevier, vol. 60(C), pages 33-42.
    4. Adam N. Elmachtoub & Michael L. Hamilton, 2021. "The Power of Opaque Products in Pricing," Management Science, INFORMS, vol. 67(8), pages 4686-4702, August.
    5. Mark Armstrong, 2016. "Nonlinear Pricing," Annual Review of Economics, Annual Reviews, vol. 8(1), pages 583-614, October.
    6. Rochet, Jean-Charles, 2024. "Multidimensional screening after 37 years," Journal of Mathematical Economics, Elsevier, vol. 113(C).
    7. Ruben Hoeksma & Marc Uetz, 2016. "Optimal Mechanism Design for a Sequencing Problem with Two-Dimensional Types," Operations Research, INFORMS, vol. 64(6), pages 1438-1450, December.
    8. Babaioff, Moshe & Gonczarowski, Yannai A. & Nisan, Noam, 2022. "The menu-size complexity of revenue approximation," Games and Economic Behavior, Elsevier, vol. 134(C), pages 281-307.

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