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Mechanism Design with Limited Information: The Case of Nonlinear Pricing

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Author Info

  • Dirk Bergemann

    ()
    (Cowles Foundation, Yale University)

  • Ji Shen

    (Department of Economics, Yale University)

  • Yun Xu

    (Dept. of Electrical Engineering, Yale University)

  • Edmund M. Yeh

    (Dept. of Electrical Engineering, Yale University)

Abstract

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.

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1775.

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Length: 12 pages
Date of creation: Nov 2010
Date of revision:
Publication status: Published in Rahul Jain and Rajgopal Kannan, eds., Game Theory for Networks. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, Vol. 75, 2012, pp. 1-10
Handle: RePEc:cwl:cwldpp:1775

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Postal: Yale University, Box 208281, New Haven, CT 06520-8281 USA
Phone: (203) 432-3702
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Web page: http://cowles.econ.yale.edu/
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

Related research

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

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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.

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