COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1775

Mechanism Design with Limited Information:
The Case of Nonlinear Pricing

Dirk Bergemann, Ji Shen, Yun Xu, and Edward M. Yeh

November 2010

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/n² as n becomes large.

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

JEL Classification: D82, D83, D86