A two-dimensional problem of revenue maximization
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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- 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.
- Alejandro M. Manelli & Daniel R. Vincent, 2004. "Multidimensional Mechanism Design: Revenue Maximization and the Multiple-Good Monopoly," Working Papers 2004.153, Fondazione Eni Enrico Mattei.
- 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.
- Thanassoulis, John, 2004. "Haggling over substitutes," Journal of Economic Theory, Elsevier, vol. 117(2), pages 217-245, August.
- Mallesh Pai & Rakesh Vohra, 2008. "Optimal Dynamic Auctions," Discussion Papers 1461, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
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