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A two-dimensional problem of revenue maximization

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  • Lev, Omer
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0304406811000796
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Mathematical Economics.

    Volume (Year): 47 (2011)
    Issue (Month): 6 ()
    Pages: 718-727

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    Handle: RePEc:eee:mateco:v:47:y:2011:i:6:p:718-727

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    Web page: http://www.elsevier.com/locate/jmateco

    Related research

    Keywords: Auctions; Multi-dimensional mechanism design; Incentive compatibility; Mechanism design;

    References

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    1. 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.
    2. Mallesh Pai & Rakesh Vohra, 2008. "Optimal Dynamic Auctions," Discussion Papers 1461, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    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. Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
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    Cited by:
    1. Sergiu Hart & Noam Nisan, 2012. "Approximate Revenue Maximization with Multiple Items," Discussion Paper Series dp606, The Center for the Study of Rationality, Hebrew University, Jerusalem.

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