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Multi-to -one dimensional and semi-discrete screening

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  • Omar Abdul Halim
  • Brendan Pass

Abstract

We study the monopolist's screening problem with a multi-dimensional distribution of consumers and a one-dimensional space of goods. We establish general conditions under which solutions satisfy a structural condition known as nestedness, which greatly simplifies their analysis and characterization. Under these assumptions, we go on to develop a general method to solve the problem, either in closed form or with relatively simple numerical computations, and illustrate it with examples. These results are established both when the monopolist has access to only a discrete subset of the one-dimensional space of products, as well as when the entire continuum is available. In the former case, we also establish a uniqueness result.

Suggested Citation

  • Omar Abdul Halim & Brendan Pass, 2025. "Multi-to -one dimensional and semi-discrete screening," Papers 2506.21740, arXiv.org, revised Oct 2025.
    • Handle: RePEc:arx:papers:2506.21740
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    References listed on IDEAS

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    1. Figalli, Alessio & Kim, Young-Heon & McCann, Robert J., 2011. "When is multidimensional screening a convex program?," Journal of Economic Theory, Elsevier, vol. 146(2), pages 454-478, March.
    2. Alfred Galichon, 2016. "Optimal transport methods in economics," Post-Print hal-03256830, HAL.
    3. Georg Nöldeke & Larry Samuelson, 2018. "The Implementation Duality," Econometrica, Econometric Society, vol. 86(4), pages 1283-1324, July.
    4. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers Main hal-03256830, HAL.
    5. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    6. Carlier, Guillaume & Dupuis, Xavier & Rochet, Jean-Charles & Thanassoulis, John, 2024. "A general solution to the quasi linear screening problem," Journal of Mathematical Economics, Elsevier, vol. 114(C).
    7. Basov, Suren, 2001. "Hamiltonian approach to multi-dimensional screening," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 77-94, September.
    8. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    9. Alfred Galichon, 2016. "Optimal Transport Methods in Economics," Economics Books, Princeton University Press, edition 1, number 10870.
    10. Carlier, Guillaume, 2001. "A general existence result for the principal-agent problem with adverse selection," Journal of Mathematical Economics, Elsevier, vol. 35(1), pages 129-150, February.
    11. J. A. Mirrlees, 1971. "An Exploration in the Theory of Optimum Income Taxation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 38(2), pages 175-208.
    12. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    13. Alfred Galichon, 2016. "Optimal transport methods in economics," SciencePo Working papers hal-03256830, HAL.
    14. Eric Maskin & John Riley, 1984. "Monopoly with Incomplete Information," RAND Journal of Economics, The RAND Corporation, vol. 15(2), pages 171-196, Summer.
    15. Pass, Brendan, 2012. "Convexity and multi-dimensional screening for spaces with different dimensions," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2399-2418.
    16. McAfee, R. Preston & McMillan, John, 1988. "Multidimensional incentive compatibility and mechanism design," Journal of Economic Theory, Elsevier, vol. 46(2), pages 335-354, December.
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