Nonlinear Pricing with Finite Information

Dirk Bergemann, Edmund Yeh and Jinkun Zhang
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Edmund Yeh: Department of Electrical and Computer Engineering, Northeastern University
Jinkun Zhang: Department of Electrical and Computer Engineering, Northeastern University

No 2297, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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/n^2/^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/n^2.

Keywords: Mechanism Design; Nonlinear Pricing; Multi-Dimension; Multi-Product; Private Information; Limited Information; Quantization; Information Theory (search for similar items in EconPapers)
JEL-codes: D82 D83 D86 (search for similar items in EconPapers)
Pages: 42 pages
Date: 2021-08
New Economics Papers: this item is included in nep-com, nep-des, nep-isf, nep-mic, nep-ore and nep-reg
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Nonlinear pricing with finite information (2021)
Working Paper: Nonlinear Pricing with Finite Information (2015)
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