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Mechanism Design with Limited Information: The Case of Nonlinear Pricing




We analyze the canonical nonlinear pricing model with limited information. A seller offers a menu with a finite number of choices to a continuum of buyers with a continuum of possible valuations. By revealing an underlying connection to quantization theory, we derive the optimal finite menu for the socially efficient and the revenue-maximizing mechanism. In both cases, we provide an estimate of the loss resulting from the usage of a finite n-class menu. We show that the losses converge to zero at a rate proportional to 1/n^2 as n becomes large.

Suggested Citation

  • Dirk Bergemann & Ji Shen & Yun Xu & Edmund M. Yeh, 2010. "Mechanism Design with Limited Information: The Case of Nonlinear Pricing," Cowles Foundation Discussion Papers 1775, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1775

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    References listed on IDEAS

    1. Pierre-Olivier Gourinchas & Hélène Rey, 2007. "International Financial Adjustment," Journal of Political Economy, University of Chicago Press, vol. 115(4), pages 665-703, August.
    2. Norman Loayza & Klaus Schmidt-Hebbel & Luis Servén, 2000. "What Drives Private Saving Across the World?," The Review of Economics and Statistics, MIT Press, vol. 82(2), pages 165-181, May.
    3. Masson, Paul R & Bayoumi, Tamim & Samiei, Hossein, 1998. "International Evidence on the Determinants of Private Saving," World Bank Economic Review, World Bank Group, vol. 12(3), pages 483-501, September.
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    Cited by:

    1. Dirk Bergemann & Ji Shen & Yun Xu & Edmund M. Yeh, 2012. "Multi-dimensional Mechanism Design with Limited Information," Cowles Foundation Discussion Papers 1859, Cowles Foundation for Research in Economics, Yale University.

    More about this item


    Mechanism design; Limited information; Nonlinear pricing; Quantization; Lloyd-max optimality;

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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