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A two-dimensional problem of revenue maximization

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  • Lev, Omer

Abstract

We consider the problem of finding the mechanism that maximizes the revenue of a seller of multiple objects. This problem turns out to be significantly more complex than the case where there is only a single object (which was solved by Myerson, 1981). The analysis is difficult even in the simplest case studied here, where there are two exclusive objects and a single buyer, with valuations uniformly distributed on triangular domains. We show that the optimal mechanisms are piecewise linear with either 2 or 3 pieces, and obtain explicit formulas for most cases of interest.

Suggested Citation

  • Lev, Omer, 2011. "A two-dimensional problem of revenue maximization," Journal of Mathematical Economics, Elsevier, vol. 47(6), pages 718-727.
    • Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:718-727
    DOI: 10.1016/j.jmateco.2011.08.007
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    References listed on IDEAS

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    1. Krishna, Vijay, 2009. "Auction Theory," Elsevier Monographs, Elsevier, edition 2, number 9780123745071.
    2. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
    3. Manelli, Alejandro M. & Vincent, Daniel R., 2007. "Multidimensional mechanism design: Revenue maximization and the multiple-good monopoly," Journal of Economic Theory, Elsevier, vol. 137(1), pages 153-185, November.
    4. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
    5. Manelli, Alejandro M. & Vincent, Daniel R., 2006. "Bundling as an optimal selling mechanism for a multiple-good monopolist," Journal of Economic Theory, Elsevier, vol. 127(1), pages 1-35, March.
    6. Mallesh Pai & Rakesh Vohra, 2008. "Optimal Dynamic Auctions," Discussion Papers 1461, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    7. Blackorby, Charles & Dezsö Szalay, 2007. "Multidimensional Screening, Affiliation, and Full Separation," The Warwick Economics Research Paper Series (TWERPS) 802, University of Warwick, Department of Economics.
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    Cited by:

    1. Hart, Sergiu & Nisan, Noam, 2019. "Selling multiple correlated goods: Revenue maximization and menu-size complexity," Journal of Economic Theory, Elsevier, vol. 183(C), pages 991-1029.
    2. Hart, Sergiu & Nisan, Noam, 2017. "Approximate revenue maximization with multiple items," Journal of Economic Theory, Elsevier, vol. 172(C), pages 313-347.

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