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Method of Digraphs for Multi-dimensional Screening

Author

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  • Sergey Kokovin

    (National Research University Higher School of Economics, Russian Federation
    Novosibirsk State University)

  • Babu Nahata

    (University of Louisville)

Abstract

We study a general model of multi-dimensional screening for discrete types of consumers without the single-crossing condition or any other essential restrictions. Such generality motivates us to introduce graph theory into optimization by treating each combination of active constraints as a digraph. Our relaxation of the constraints (a slackness parameter) excludes bunching and cycles among the constraints. Then, the only possible solution structures are rivers, which are acyclic rooted digraphs, and the Lagrange multipliers can be used to characterize the solutions. Relying on these propositions, we propose and justify an optimization algorithm. In the experiments, its branch-and-bound version with a good starting plan shows fewer iterations than a complete search among all rivers.

Suggested Citation

  • Sergey Kokovin & Babu Nahata, 2017. "Method of Digraphs for Multi-dimensional Screening," Annals of Operations Research, Springer, vol. 253(1), pages 431-451, June.
    • Handle: RePEc:spr:annopr:v:253:y:2017:i:1:d:10.1007_s10479-016-2320-3
    DOI: 10.1007/s10479-016-2320-3
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    References listed on IDEAS

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    1. Brito, Dagobert L, et al, 1990. "Pareto Efficient Tax Structures," Oxford Economic Papers, Oxford University Press, vol. 42(1), pages 61-77, January.
    2. Rachel R. Chen & Esther Gal-Or & Paolo Roma, 2014. "Opaque Distribution Channels for Competing Service Providers: Posted Price vs. Name-Your-Own-Price Mechanisms," Operations Research, INFORMS, vol. 62(4), pages 733-750, August.
    3. Babu Nahata & Serguei Kokovin & Evgeny Zhelobodko, 2003. "Self-Selection Under Non-Ordered Valuations: Type-Splitting, Envy-Cycles, Rationing And Efficiency," General Economics and Teaching 0307001, University Library of Munich, Germany.
    4. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871525, October.
    5. Araujo, Aloisio & Moreira, Humberto, 2010. "Adverse selection problems without the Spence-Mirrlees condition," Journal of Economic Theory, Elsevier, vol. 145(3), pages 1113-1141, May.
    6. Jullien, Bruno, 2000. "Participation Constraints in Adverse Selection Models," Journal of Economic Theory, Elsevier, vol. 93(1), pages 1-47, July.
    7. Hugh Everett, 1963. "Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources," Operations Research, INFORMS, vol. 11(3), pages 399-417, June.
    8. Guesnerie, Roger & Seade, Jesus, 1982. "Nonlinear pricing in a finite economy," Journal of Public Economics, Elsevier, vol. 17(2), pages 157-179, March.
    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. Mark Armstrong & Robert Porter (ed.), 2007. "Handbook of Industrial Organization," Handbook of Industrial Organization, Elsevier, edition 1, volume 3, number 1.
    11. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2006. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692083, October.
    12. 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.
    13. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    14. 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.
    15. Kokovin, Sergey & Nahata, Babu & Zhelobodko, Evgeny, 2013. "Dupuit conjecture for constrained screening: Overall distortion and type-partitioning," Economics Letters, Elsevier, vol. 118(3), pages 439-441.
    16. Bonatti, Alessandro, 2011. "Brand-specific tastes for quality," International Journal of Industrial Organization, Elsevier, vol. 29(5), pages 562-575, September.
    17. Stole, Lars A., 2007. "Price Discrimination and Competition," Handbook of Industrial Organization, in: Mark Armstrong & Robert Porter (ed.), Handbook of Industrial Organization, edition 1, volume 3, chapter 34, pages 2221-2299, Elsevier.
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