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Nonlinear Pricing with Finite Information

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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.

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  • Dirk Bergemann & Edmund Yeh & Jinkun Zhang, 2021. "Nonlinear Pricing with Finite Information," Cowles Foundation Discussion Papers 2297, Cowles Foundation for Research in Economics, Yale University.
    • Handle: RePEc:cwl:cwldpp:2297
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    1. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
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    3. Bergemann, Dirk & Yeh, Edmund & Zhang, Jinkun, 2021. "Nonlinear pricing with finite information," Games and Economic Behavior, Elsevier, vol. 130(C), pages 62-84.
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    Cited by:

    1. Dirk Bergemann & Marco Ottaviani, 2021. "Information Markets and Nonmarkets," Cowles Foundation Discussion Papers 2296, Cowles Foundation for Research in Economics, Yale University.
    2. Dirk Bergemann & Alessandro Bonatti & Andreas Haupt & Alex Smolin, 2021. "The Optimality of Upgrade Pricing," Papers 2107.10323, arXiv.org, revised Dec 2021.
    3. Bergemann, Dirk & Yeh, Edmund & Zhang, Jinkun, 2021. "Nonlinear pricing with finite information," Games and Economic Behavior, Elsevier, vol. 130(C), pages 62-84.

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    More about this item

    Keywords

    Mechanism Design; Nonlinear Pricing; Multi-Dimension; Multi-Product; Private Information; Limited Information; Quantization; Information Theory;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D83 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Search; Learning; Information and Knowledge; Communication; Belief; Unawareness
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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