Multi-dimensional Mechanism Design with Limited Information

Dirk Bergemann, Ji Shen, Yun Xu and Edmund M. Yeh
Additional contact information
Ji Shen: Dept. of Finance, London School of Economics
Yun Xu: Dept. of Electrical Engineering, Yale University
Edmund M. Yeh: Dept. of Computer Science and Electrical Engineering, Northeastern University

No 1859, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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 R_d^+ 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.

Keywords: Mechanism design; Multi-dimensional private information; Limited information; Nonlinear pricing; Quantization; Information theory (search for similar items in EconPapers)
JEL-codes: C72 C73 D43 D83 (search for similar items in EconPapers)
Pages: 22 pages
Date: 2012-04
New Economics Papers: this item is included in nep-cta and nep-mic
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Published in 13th ACM Conference on Electronic Commerce (EC '12)

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