Nonlinear pricing with finite information

Dirk Bergemann, Edmund Yeh, Jinkun Zhang

Abstract: 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.

External IDs:dblp:journals/geb/BergemannYZ21