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Robust mechanisms: the curvature case

Vinicius Carrasco (), Vitor Farinha Luz (), Paulo Monteiro and Humberto Moreira ()
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Vinicius Carrasco: PUC–Rio
Vitor Farinha Luz: The University of British Columbia
Humberto Moreira: FGV EPGE, Brazilian School of Economics and Finance

Economic Theory, 2019, vol. 68, issue 1, No 7, 203-222

Abstract: 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.

Keywords: Robust mechanism design; Monopolistic screening under uncertainty; Principal–agent model; D82; D86 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s00199-018-1120-1

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