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All Solution Graphs in Multidimensional Screening

Author

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  • 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)

Abstract

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.

Suggested Citation

  • 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.
    • Handle: RePEc:nea:journl:y:2011:i:11:p:10-38
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    References listed on IDEAS

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    10. 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.
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    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.
    2. Sergey Kokovin & Babu Nahata, 2017. "Method of Digraphs for Multi-dimensional Screening," Annals of Operations Research, Springer, vol. 253(1), pages 431-451, June.
    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.
    5. Yong Chao & Babu Nahata, 2018. "Market foreclosure, output and welfare under second-degree price discrimination," Economics Bulletin, AccessEcon, vol. 38(4), pages 2116-2127.

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    More about this item

    Keywords

    incentive compatibility; multidimensional screening; second-degree price discrimination; non-linear pricing; graphs;
    All these keywords.

    JEL classification:

    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • L10 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - General
    • L12 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Monopoly; Monopolization Strategies
    • L40 - Industrial Organization - - Antitrust Issues and Policies - - - General

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