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All solution graphs in multidimensional screening


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


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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  • Kokovin, Sergey & Nahata, Babu & Zhelobodko, Evgeny, 2010. "All solution graphs in multidimensional screening," MPRA Paper 30025, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:30025

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    References listed on IDEAS

    1. 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.
    2. Brito, Dagobert L, et al, 1990. "Pareto Efficient Tax Structures," Oxford Economic Papers, Oxford University Press, vol. 42(1), pages 61-77, January.
    3. Armstrong, Mark, 2006. "Price discrimination," MPRA Paper 4693, University Library of Munich, Germany.
    4. Andersson, Tommy, 2005. "Profit maximizing nonlinear pricing," Economics Letters, Elsevier, vol. 88(1), pages 135-139, July.
    5. Guesnerie, Roger & Seade, Jesus, 1982. "Nonlinear pricing in a finite economy," Journal of Public Economics, Elsevier, vol. 17(2), pages 157-179, March.
    6. Babu Nahata & Serguei Kokovin & Evgeny Zhelobodko, 2003. "Package Sizes, Tariffs, Quantity Discount and Premium," General Economics and Teaching 0307002, EconWPA.
    7. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    8. 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.
    9. 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.
    10. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, Elsevier.
    11. 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.
    12. 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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    1. repec:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2320-3 is not listed on IDEAS
    2. 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.
    3. Sergey Kokovin & Babu Nahata & Evgeny Zhelobodko, 2014. "Distortion in Screening and Spatial Preferences," HSE Working papers WP BRP 83/EC/2014, National Research University Higher School of Economics.
    4. Kimmo Berg, 2013. "Complexity of solution structures in nonlinear pricing," Annals of Operations Research, Springer, vol. 206(1), pages 23-37, July.

    More about this item


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

    JEL classification:

    • L11 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Production, Pricing, and Market Structure; Size Distribution of Firms
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly

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