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Multi-Dimensional Mechanism Design with Limited Information

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  • Dirk Bergemann
  • Ji Shen
  • Yun Xu
  • Edmund M. Yeh

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.

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Paper provided by David K. Levine in its series Levine's Working Paper Archive with number 786969000000000559.

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Date of creation: 11 Sep 2012
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Handle: RePEc:cla:levarc:786969000000000559

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  1. Bergemann, Dirk & Pesendorfer, Martin, 2001. "Information Structures in Optimal Auctions," CEPR Discussion Papers 2991, C.E.P.R. Discussion Papers.
  2. Heidrun Hoppe & Benny Moldovanu & Emre Ozdenoren, 2011. "Coarse matching with incomplete information," Economic Theory, Springer, vol. 47(1), pages 75-104, May.
  3. Dirk Bergemann & Ji Shen & Yun Xu & Edmund M. Yeh, 2010. "Mechanism Design with Limited Information: The Case of Nonlinear Pricing," Cowles Foundation Discussion Papers 1775, Cowles Foundation for Research in Economics, Yale University.
  4. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  5. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
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