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Robust Mechanisms: the curvature case

Author

Listed:
  • Vinicius Carrasco

    (Department of Economics PUC-Rio)

  • Vitor Farinha Luz

    (European University Institute and the Department of Economics, The University of British Columbia)

  • Paulo Monteiro

    (FGV/EPGE)

  • Humberto Moreira

    (FGV/EPGE)

Abstract

This note considers the problem of a principal (she) who faces a privately informed agent (he) and only knows one moment of the distribution from which his types are drawn. Payoffs are non-linear in the allocation and the principal maximizes her worst-case expected profits. We recast the robust design problem as a zero-sum game played by the principal and an adversarial nature who seeks to minimize her expected payoffs. The robust mechanism and the worst case distribution are, then, the Nash equilibrium of such game. A robustness property of the optimal mechanism imposes restrictions on the principal’s ex-post profit function. These restrictions then lead to the optimal mechanism. The robust mechanism entails exclusion of low types and distortions at the intensive margin that (in a precise sense) are larger than what those that prevail in standard Bayesian mechanism design problems.

Suggested Citation

  • Vinicius Carrasco & Vitor Farinha Luz & Paulo Monteiro & Humberto Moreira, 2015. "Robust Mechanisms: the curvature case," Textos para discussão 642, Department of Economics PUC-Rio (Brazil).
    • Handle: RePEc:rio:texdis:642
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    References listed on IDEAS

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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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    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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