Abstract

http://ssrn.com/abstract=2041968
 


 



Multi-Dimensional Mechanism Design with Limited Information


Dirk Bergemann


Yale University - Cowles Foundation - Department of Economics

Ji Shen


London School of Economics & Political Science (LSE)

Yun Xu


affiliation not provided to SSRN

Edmund M. Yeh


affiliation not provided to SSRN

April 18, 2012

Cowles Foundation Discussion Paper No. 1859

Abstract:     
We analyze a nonlinear pricing model with limited information. Each buyer can purchase a large variety, d, of goods. His preference for each good is represented by a scalar and his preference over d goods is represented by a d-dimensional vector. The type space of each buyer is given by a compact subset of Rd with a continuum of possible types. By contrast, the seller is limited to offer a finite number M of d-dimensional choices.

We provide necessary conditions that the optimal finite menu of the social welfare maximizing problem has to satisfy. We establish an underlying connection to the theory of quantization and provide an estimate of the welfare loss resulting from the usage of the d-dimensional M-class menu. We show that the welfare loss converges to zero at a rate proportional to d/M^{2/d}.

We show that in higher dimensions, a significant reduction in the welfare loss arises from an optimal partition of the d-dimensional type space that takes advantage of the correlation among the d parameters.

Number of Pages in PDF File: 23

Keywords: Mechanism design, Multi-dimensional private information, Limited information, Nonlinear pricing, Quantization, Information theory

JEL Classification: C72, C73, D43, D83

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Date posted: April 19, 2012  

Suggested Citation

Bergemann, Dirk and Shen, Ji and Xu, Yun and Yeh, Edmund M., Multi-Dimensional Mechanism Design with Limited Information (April 18, 2012). Cowles Foundation Discussion Paper No. 1859. Available at SSRN: http://ssrn.com/abstract=2041968 or http://dx.doi.org/10.2139/ssrn.2041968

Contact Information

Dirk Bergemann (Contact Author)
Yale University - Cowles Foundation - Department of Economics ( email )
28 Hillhouse Ave
New Haven, CT 06520-8268
United States
203-432-3592 (Phone)
203-432-2128 (Fax)
HOME PAGE: http://www.econ.yale.edu/~dirk/
Ji Shen
London School of Economics & Political Science (LSE) ( email )
Yun Xu
affiliation not provided to SSRN ( email )
Edmund M. Yeh
affiliation not provided to SSRN ( email )
Feedback to SSRN


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