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The menu-size complexity of revenue approximation

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  • Babaioff, Moshe
  • Gonczarowski, Yannai A.
  • Nisan, Noam

Abstract

Consider a monopolist selling n items to an additive buyer whose item values are drawn from independent distributions F1,F2,…,Fn possibly having unbounded support. Unlike in the single-item case, it is well known that the revenue-optimal selling mechanism (a pricing scheme) may be complex, sometimes requiring a continuum of menu entries. Also known is that simple mechanisms with a bounded number of menu entries can extract a constant fraction of the optimal revenue. Nonetheless, whether an arbitrarily high fraction of the optimal revenue can be extracted via a bounded menu size remained open.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:gamebe:v:134:y:2022:i:c:p:281-307
    DOI: 10.1016/j.geb.2021.03.001
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    References listed on IDEAS

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    1. Sergiu Hart & Noam Nisan, 2013. "The Menu-Size Complexity of Auctions," Discussion Paper Series dp637, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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    4. 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.
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    6. 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. Ran Canetti & Amos Fiat & Yannai A. Gonczarowski, 2023. "Zero-Knowledge Mechanisms," Papers 2302.05590, arXiv.org.
    2. Yannai A. Gonczarowski & Clayton Thomas, 2022. "Structural Complexities of Matching Mechanisms," Papers 2212.08709, arXiv.org, revised Mar 2024.
    3. Yannai A. Gonczarowski & Ori Heffetz & Clayton Thomas, 2022. "Strategyproofness-Exposing Mechanism Descriptions," Papers 2209.13148, arXiv.org, revised Jul 2023.

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