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All solution graphs in multidimensional screening

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  • Kokovin, Sergey
  • Nahata, Babu
  • Zhelobodko, Evgeny

Abstract

We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentive-compatibility constraints. Any active (becoming equality) constraint can be perceived as "envy" arc from one type to another, so the set of active constraints is a digraph. We find that: (1) any solution has an in-rooted acyclic graph ("river"); (2) for any logically feasible river there exists a screening problem resulting in such river. Using these results, any solution is characterized both through its spanning-tree and through its Lagrange multipliers, that can help in finding solutions and their efficiency/distortion properties.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 30025.

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Date of creation: Nov 2010
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Handle: RePEc:pra:mprapa:30025

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Related research

Keywords: incentive compatibility; multidimensional screening; second-degree price discrimination; non-linear pricing; graphs;

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References

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  1. Babu Nahata & Serguei Kokovin & Evgeny Zhelobodko, 2003. "Package Sizes, Tariffs, Quantity Discount and Premium," General Economics and Teaching 0307002, EconWPA.
  2. Dagobert L. Brito & Jonathan H. Hamilton & Steven M. Slutsky & Joseph E. Stiglitz, 1990. "Pareto Efficient Tax Structures," NBER Working Papers 3288, National Bureau of Economic Research, Inc.
  3. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, Elsevier.
  4. Armstrong, Mark & Rochet, Jean-Charles, 1999. "Multi-dimensional screening:: A user's guide," European Economic Review, Elsevier, vol. 43(4-6), pages 959-979, April.
  5. Kokovin, Sergey & Nahata, Babu & Zhelobodko, Evgeny, 2010. "All solution graphs in multidimensional screening," MPRA Paper 30025, University Library of Munich, Germany.
  6. Guesnerie Roger & Seade Jesus, 1981. "Nonlinear pricing in a finite economy," CEPREMAP Working Papers (Couverture Orange) 8118, CEPREMAP.
  7. Rochet, Jean-Charles, 1987. "A necessary and sufficient condition for rationalizability in a quasi-linear context," Journal of Mathematical Economics, Elsevier, vol. 16(2), pages 191-200, April.
  8. Kokovin, Sergey & Nahata, Babu & Zhelobodko, Evgeny, 2010. "Multidimensional screening under nonlinear costs: Limits of standard approach," Economics Letters, Elsevier, vol. 107(2), pages 263-265, May.
  9. Andersson, Tommy, 2005. "Profit maximizing nonlinear pricing," Economics Letters, Elsevier, vol. 88(1), pages 135-139, July.
  10. Andersson, Tommy, 2008. "Efficiency properties of non-linear pricing schedules without the single-crossing condition," Economics Letters, Elsevier, vol. 99(2), pages 364-366, May.
  11. Brito, Dagobert L, et al, 1990. "Pareto Efficient Tax Structures," Oxford Economic Papers, Oxford University Press, vol. 42(1), pages 61-77, January.
  12. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
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Cited by:
  1. Kokovin, S. & Nahata, B. & Zhelobodko, E., 2011. "All Solution Graphs in Multidimensional Screening," Journal of the New Economic Association, New Economic Association, issue 11, pages 10-38.

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