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.