Mechanism Design with Limited Information: The Case of Nonlinear Pricing

Dirk Bergemann; Ji Shen; Yun Xu; Edmund Yeh

Game Theory for Networks. 2nd International ICST Conference, GAMENETS 2011, Shanghai, China, April 16-18, 2011, Revised Selected Papers

Research Article

Mechanism Design with Limited Information: The Case of Nonlinear Pricing

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@INPROCEEDINGS{10.1007/978-3-642-30373-9_1,
    author={Dirk Bergemann and Ji Shen and Yun Xu and Edmund Yeh},
    title={Mechanism Design with Limited Information: The Case of Nonlinear Pricing},
    proceedings={Game Theory for Networks. 2nd International ICST Conference, GAMENETS 2011, Shanghai, China, April 16-18, 2011, Revised Selected Papers},
    proceedings_a={GAMENETS},
    year={2012},
    month={10},
    keywords={Mechanism Design Limited Information Nonlinear Pricing Quantization Lloyd-Max Optimality},
    doi={10.1007/978-3-642-30373-9_1}
}

Dirk Bergemann
Ji Shen
Yun Xu
Edmund Yeh
Year: 2012
Mechanism Design with Limited Information: The Case of Nonlinear Pricing
GAMENETS
Springer
DOI: 10.1007/978-3-642-30373-9_1

Dirk Bergemann¹^,*, Ji Shen¹, Yun Xu¹^,*, Edmund Yeh¹^,*

1: Yale University

*Contact email: dirk.bergemann@yale.edu, yun.xu@yale.edu, edmund.yeh@yale.edu

Abstract

We analyze the canonical nonlinear pricing model with limited information. A seller offers a menu with a finite number of choices to a continuum of buyers with a continuum of possible valuations. By revealing an underlying connection to quantization theory, we derive the optimal finite menu for the socially efficient and the revenue-maximizing mechanism. In both cases, we provide an estimate of the loss resulting from the usage of a finite -class menu. We show that the losses converge to zero at a rate proportional to 1/ as becomes large.

Keywords: Mechanism Design Limited Information Nonlinear Pricing Quantization Lloyd-Max Optimality

Published: 2012-10-08

: http://dx.doi.org/10.1007/978-3-642-30373-9_1