Mechanism Design with Limited Information: The Case of Nonlinear Pricing

13 Pages Posted: 30 Nov 2010

See all articles by Dirk Bergemann

Dirk Bergemann

Yale University - Cowles Foundation - Department of Economics; Yale University - Cowles Foundation

Ji Shen

London School of Economics & Political Science (LSE)

Yun Xu

Yale University

Edmund M. Yeh

Northeastern University

Date Written: November 30, 2010

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.

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

JEL Classification: D82, D83, D86

Suggested Citation

Bergemann, Dirk and Shen, Ji and Xu, Yun and Yeh, Edmund M., Mechanism Design with Limited Information: The Case of Nonlinear Pricing (November 30, 2010). Cowles Foundation Discussion Paper No. 1775. Available at SSRN: https://ssrn.com/abstract=1717904 or http://dx.doi.org/10.2139/ssrn.1717904

Dirk Bergemann (Contact Author)

Yale University - Cowles Foundation - Department of Economics ( email )

28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3592 (Phone)
203-432-2128 (Fax)

HOME PAGE: http://www.econ.yale.edu/~dirk/

Yale University - Cowles Foundation

Box 208281
New Haven, CT 06520-8281
United States

Ji Shen

London School of Economics & Political Science (LSE) ( email )

Houghton Street
London, WC2A 2AE
United Kingdom

Yun Xu

Yale University ( email )

New Haven, CT 06520
United States

Edmund M. Yeh

Northeastern University ( email )

Boston, MA 02115
United States

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