Nonlinear Pricing with Finite Information

Dirk Bergemann, Ji Shen, Yun Xu and Edmund M. Yeh
Additional contact information
Ji Shen: Dept. of Finance, London School of Economics
Yun Xu: Dept. of Electrical Engineering, Yale University
Edmund M. Yeh: Dept. of Computer Science and Electrical Engineering, Northeastern University

No 1981, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: We analyze nonlinear pricing with finite information. A seller offers a menu to a continuum of buyers with a continuum of possible valuations. The menu is limited to offering a finite number of choices representing a finite communication capacity between buyer and seller. We identify necessary conditions that the optimal finite menu must satisfy, either for the socially efficient or for the revenue-maximizing mechanism. These conditions require that information be bundled, or "quantized" optimally. We show that the loss resulting from using the n-item menu converges to zero at a rate proportional to 1 = n^2. We extend our model to 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. By using repeated scalar quantization, we show that the losses resulting from using the d-dimensional n-class menu converge to zero at a rate proportional to d = n^{2/d}. We introduce vector quantization and establish that the losses due to finite menus are significantly reduced by offering optimally chosen bundles.

Keywords: Mechanism design; Nonlinear pricing; Multi-Dimension; Multi-product; Private information; Limited information; Quantization; Information theory (search for similar items in EconPapers)
JEL-codes: C72 C73 D43 D83 (search for similar items in EconPapers)
Pages: 37 pages
Date: 2015-01
New Economics Papers: this item is included in nep-com, nep-cta, nep-mic and nep-mkt
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Journal Article: Nonlinear pricing with finite information (2021)
Working Paper: Nonlinear Pricing with Finite Information (2021)
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