CFDP 2297

Nonlinear Pricing with Finite Information


Publication Date: August 2021

Pages: 42


We analyze nonlinear pricing with finite information. We consider a multi-product environment where each buyer has preferences over a d-dimensional variety of goods. The seller is limited to offering a finite number n of d-dimensional choices. The limited menu reflects a finite communication capacity between the buyer and seller.
We identify necessary conditions that the optimal finite menu must satisfy, for either the socially efficient or the revenue-maximizing mechanism. These conditions require that information be bundled, or “quantized,” optimally.
We introduce vector quantization and establish that the losses due to finite menus converge to zero at a rate of 1/n2/d. In the canonical model with one-dimensional products and preferences, this establishes that the loss resulting from using the n-item menu converges to zero at a rate proportional to 1/n2.

Keywords: Mechanism Design, Nonlinear Pricing, Multi-Dimension, Multi-Product, Private Information, Limited Information, Quantization, Information Theory

JEL Classification Codes: D82, D83, D86

JEL Classification Codes: D82D83D86

See CFP: CFP1742

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