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Robust mechanisms: the curvature case

Author

Listed:
  • Vinicius Carrasco

    (PUC–Rio)

  • Vitor Farinha Luz

    (The University of British Columbia)

  • Paulo K. Monteiro

    (FGV EPGE, Brazilian School of Economics and Finance)

  • Humberto Moreira

    (FGV EPGE, Brazilian School of Economics and Finance)

Abstract

This paper considers the problem of a Principal who faces a privately informed Agent and only knows one moment of the type’s distribution. Preferences are nonlinear in the allocation, and the Principal maximizes her worst-case expected profits. The robustness property of the optimal mechanism imposes restrictions on the Principal’s ex-post payoff function: subject to the allocation being nonzero, ex-post payoffs are linear in the Agent’s type. The robust mechanism entails exclusion of low types, distortions at the intensive margin and efficiency at the top. We show that, under some conditions, distortions in the optimal mechanism are decreasing in types. This monotonicity has relevant consequences for several applications discussed. Our characterization uses an auxiliary zero-sum game played by the Principal and an adversarial Nature who seeks to minimize her expected payoffs which also gives us a characterization of the worst-case distribution from the Principal’s perspective. Applications of our framework to insurance provision, optimal taxation, nonlinear pricing and regulation are discussed.

Suggested Citation

  • Vinicius Carrasco & Vitor Farinha Luz & Paulo K. Monteiro & Humberto Moreira, 2019. "Robust mechanisms: the curvature case," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 68(1), pages 203-222, July.
    • Handle: RePEc:spr:joecth:v:68:y:2019:i:1:d:10.1007_s00199-018-1120-1
    DOI: 10.1007/s00199-018-1120-1
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    Cited by:

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    2. Eitan Sapiro-Gheiler, 2021. "Persuasion with Ambiguous Receiver Preferences," Papers 2109.11536, arXiv.org, revised Aug 2023.
    3. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    4. Zhiwei Liu & Nicholas C. Yannelis, 2021. "Persuasion in an asymmetric information economy: a justification of Wald’s maxmin preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 801-833, October.
    5. Li, Zhaolin, 2021. "Robust Moral Hazard with Distributional Ambiguity," Working Papers BAWP-2021-01, University of Sydney Business School, Discipline of Business Analytics.
    6. Rosenthal, Maxwell, 2023. "Robust incentives for risk," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    7. Li, Zhaolin, 2020. "Robust Moral Hazard with Distributional Ambiguity," Working Papers BAWP-2020-03, University of Sydney Business School, Discipline of Business Analytics.

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