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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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    1. Liran Einav & Amy Finkelstein & Stephen P. Ryan & Paul Schrimpf & Mark R. Cullen, 2013. "Selection on Moral Hazard in Health Insurance," American Economic Review, American Economic Association, vol. 103(1), pages 178-219, February.
    2. , & , & ,, 2006. "Optimal auctions with ambiguity," Theoretical Economics, Econometric Society, vol. 1(4), pages 411-438, December.
    3. Nenad Kos & Matthias Messner, 2015. "Selling to the mean," Working Papers 551, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
    4. Laffont, Jean-Jacques & Tirole, Jean, 1986. "Using Cost Observation to Regulate Firms," Journal of Political Economy, University of Chicago Press, vol. 94(3), pages 614-641, June.
    5. Vinicius Carrasco & Vitor Farinha Luz & Paulo Monteiro & Humberto Moreira, 2015. "Robust Selling Mechanisms," Textos para discussão 641, Department of Economics PUC-Rio (Brazil).
    6. Alexander Frankel, 2014. "Aligned Delegation," American Economic Review, American Economic Association, vol. 104(1), pages 66-83, January.
    7. Gabriel Carroll, 2017. "Robustness and Separation in Multidimensional Screening," Econometrica, Econometric Society, vol. 85, pages 453-488, March.
    8. Carroll, Gabriel, 2016. "Informationally robust trade and limits to contagion," Journal of Economic Theory, Elsevier, vol. 166(C), pages 334-361.
    9. Mussa, Michael & Rosen, Sherwin, 1978. "Monopoly and product quality," Journal of Economic Theory, Elsevier, vol. 18(2), pages 301-317, August.
    10. Dirk Bergemann & Karl Schlag, 2012. "Robust Monopoly Pricing," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 13, pages 417-441, World Scientific Publishing Co. Pte. Ltd..
    11. Dirk Bergemann & Karl H. Schlag, 2012. "Pricing Without Priors," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 12, pages 405-415, World Scientific Publishing Co. Pte. Ltd..
    12. Garrett, Daniel F., 2014. "Robustness of simple menus of contracts in cost-based procurement," Games and Economic Behavior, Elsevier, vol. 87(C), pages 631-641.
    13. Wolitzky, Alexander, 2016. "Mechanism design with maxmin agents: theory and an application to bilateral trade," Theoretical Economics, Econometric Society, vol. 11(3), September.
    14. 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.
    15. Leonid Hurwicz & Leonard Shapiro, 1978. "Incentive Structures Maximizing Residual Gain under Incomplete Information," Bell Journal of Economics, The RAND Corporation, vol. 9(1), pages 180-191, Spring.
    16. Gabriel Carroll, 2015. "Robustness and Linear Contracts," American Economic Review, American Economic Association, vol. 105(2), pages 536-563, February.
    17. Roger B. Myerson, 1981. "Optimal Auction Design," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 58-73, February.
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    3. Eitan Sapiro-Gheiler, 2021. "Persuasion with Ambiguous Receiver Preferences," Papers 2109.11536, arXiv.org, revised Aug 2023.
    4. Rosenthal, Maxwell, 2023. "Robust incentives for risk," Journal of Mathematical Economics, Elsevier, vol. 109(C).
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    6. Wanchang Zhang, 2021. "Random Double Auction: A Robust Bilateral Trading Mechanism," Papers 2105.05427, arXiv.org, revised May 2022.
    7. 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.

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