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All Solution Graphs in Multidimensional Screening

  • Kokovin, S.

    (Sobolev Institute of Mathematics SBRAS and Novosibirsk State University, Novosibirsk, Russia
    Saint Petersburg branch of National Research University High School of Economics, Saint Petersburg, Russia)

  • Nahata, B.

    (Department of Economics University of Louisville, Louisville, Kentucky,USA)

  • Zhelobodko, E.

    (Department of Economics, Novosibirsk State University, Novosibirsk, Russia
    Saint Petersburg branch of National Research University High School of Economics, Saint Petersburg, Russia)

We study general discrete-types multidimensional screening without any noticeable restrictions on valuations, using instead epsilon-relaxation of the incentivecompatibility 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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Article provided by New Economic Association in its journal Journal of the New Economic Association.

Volume (Year): (2011)
Issue (Month): 11 ()
Pages: 10-38

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Handle: RePEc:nea:journl:y:2011:i:11:p:10-38
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  1. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
  2. 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.
  3. Babu Nahata & Serguei Kokovin & Evgeny Zhelobodko, 2003. "Package Sizes, Tariffs, Quantity Discount and Premium," General Economics and Teaching 0307002, EconWPA.
  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. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, Elsevier.
  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. 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.
  10. Andersson, Tommy, 2005. "Profit maximizing nonlinear pricing," Economics Letters, Elsevier, vol. 88(1), pages 135-139, July.
  11. 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.
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