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Screening with an approximate type space

  • Kristóf Madarász
  • Andrea Prat

Consider a standard single-agent quasilinear mechanism design problem with a potentially large type space. We wish to provide an upper bound to the principal’s payoff loss if she operates on the basis of a discrete approximation rather than the true type space. We show that, if the principal simply uses the mechanism that is optimal for the approximate type space, the loss cannot be bound even as the approximate type space converges to the true one. We propose instead the Profit-Participation algorithm, whereby the principal first computes the optimal mechanism for the approximate type but then she discounts the resulting prices in a way that is proportional to her payoff under the approximate type space for each possible allocation. We bound the principal’s payoff loss and show that it vanishes as approximate type space converges to the true one. We apply our results to situations where the principal faces: (i) computation costs; (ii) search costs; or (iii) model uncertainty.

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File URL: http://eprints.lse.ac.uk/35056/
File Function: Open access version.
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Paper provided by London School of Economics and Political Science, LSE Library in its series LSE Research Online Documents on Economics with number 35056.

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Length: 28 pages
Date of creation: 15 Mar 2010
Date of revision:
Handle: RePEc:ehl:lserod:35056
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Web page: http://www.lse.ac.uk/

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  1. Dirk Bergemann & Karl Schlag, 2005. "Robust Monopoly Pricing," Cowles Foundation Discussion Papers 1527RR, Cowles Foundation for Research in Economics, Yale University, revised Sep 2008.
  2. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  3. Nisan, Noam & Segal, Ilya, 2006. "The communication requirements of efficient allocations and supporting prices," Journal of Economic Theory, Elsevier, vol. 129(1), pages 192-224, July.
  4. Armstrong, Mark, 1999. "Price Discrimination by a Many-Product Firm," Review of Economic Studies, Wiley Blackwell, vol. 66(1), pages 151-68, January.
  5. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
  6. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
  7. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
  8. Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
  9. Gregory Dobson & Shlomo Kalish, 1993. "Heuristics for Pricing and Positioning a Product-Line Using Conjoint and Cost Data," Management Science, INFORMS, vol. 39(2), pages 160-175, February.
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