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A necessary optimality condition in two-dimensional screening

Author

Listed:
  • Aloisio Araujo

    (IMPA
    FGV EPGE, Brazilian School of Economics and Finance)

  • Sergei Vieira

    (Ibmec, Av. Presidente Wilson 118)

  • Braulio Calagua

    (UDEP)

Abstract

This paper studies adverse selection problems with a one-dimensional principal instrument and a two-dimensional agent type. We provide an optimality condition that characterizes the bunching of continuum types. The approach is based on a reparameterization of the type space in terms of the endogenous optimal allocation level curves. The condition obtained is related with the optimality of two pooling types in the one-dimensional screening without the single-crossing. We illustrate the method by analyzing one example from the literature as well as a new example far from the linear-quadratic case

Suggested Citation

  • Aloisio Araujo & Sergei Vieira & Braulio Calagua, 2022. "A necessary optimality condition in two-dimensional screening," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 781-806, April.
    • Handle: RePEc:spr:joecth:v:73:y:2022:i:2:d:10.1007_s00199-021-01352-x
    DOI: 10.1007/s00199-021-01352-x
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    References listed on IDEAS

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    1. Nicholas Yannelis, 2009. "Debreu’s social equilibrium theorem with asymmetric information and a continuum of agents," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 38(2), pages 419-432, February.
    2. 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.
    3. Bruno Biais & David Martimort & Jean-Charles Rochet, 2000. "Competing Mechanisms in a Common Value Environment," Econometrica, Econometric Society, vol. 68(4), pages 799-838, July.
    4. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    5. Basov, Suren, 2001. "Hamiltonian approach to multi-dimensional screening," Journal of Mathematical Economics, Elsevier, vol. 36(1), pages 77-94, September.
    6. Monteiro, Paulo K. & Page Jr., Frank H., 1998. "Optimal selling mechanisms for multiproduct monopolists: incentive compatibility in the presence of budget constraints," Journal of Mathematical Economics, Elsevier, vol. 30(4), pages 473-502, November.
    7. Armstrong, Mark, 1996. "Multiproduct Nonlinear Pricing," Econometrica, Econometric Society, vol. 64(1), pages 51-75, January.
    8. Paul Milgrom & Ilya Segal, 2002. "Envelope Theorems for Arbitrary Choice Sets," Econometrica, Econometric Society, vol. 70(2), pages 583-601, March.
    9. 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.
    10. Jean-Charles Rochet & Philippe Chone, 1998. "Ironing, Sweeping, and Multidimensional Screening," Econometrica, Econometric Society, vol. 66(4), pages 783-826, July.
    11. Kelvin Shuangjian Zhang, 2019. "Existence in multidimensional screening with general nonlinear preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 67(2), pages 463-485, March.
    12. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    13. 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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    Cited by:

    1. Braulio Calagua, 2023. "Reducing incentive constraints in bidimensional screening," The Journal of Mechanism and Institution Design, Society for the Promotion of Mechanism and Institution Design, University of York, vol. 8(1), pages 107-150, December.
    2. Rabah Amir & Bernard Cornet & M. Ali Khan & David Levine & Edward C. Prescott, 2022. "Special Issue in honor of Nicholas C. Yannelis – Part II," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 377-385, April.

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    More about this item

    Keywords

    Two-dimensional screening; Bunching; Non single-crossing; Quasilinear equation; Characteristic curves;
    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

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