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Robust Mechanisms: The Curvature Case

18 Pages Posted: 1 Apr 2017  

Vinicius Carrasco

Independent

Vitor Farinha Luz

University of British Columbia

Paulo Klinger Monteiro Sr.

Getulio Vargas Foundation (FGV) - EPGE

Humberto Moreira

Fundacao Getulio Vargas (FGV)

Date Written: March 1, 2017

Abstract

This paper considers the problem of a principal (she) who faces a privately informed agent (he) and only knows one moment of the type distribution. Preferences are nonlinear in the allocation and the principal maximizes her worst-case expected profits. A robustness property of the optimal mechanism imposes restrictions on the principal’s ex-post payoff function: conditional on the allocation being non-zero, 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 additional assumptions, distortions in the optimal mechanism are decreasing with 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, non-linear pricing and regulation are discussed.

Keywords: Robust Mechanism Design, Monopolistic Screening under Uncertainty

JEL Classification: D82, D86

Suggested Citation

Carrasco, Vinicius and Farinha Luz, Vitor and Monteiro, Paulo Klinger and Moreira, Humberto, Robust Mechanisms: The Curvature Case (March 1, 2017). Available at SSRN: https://ssrn.com/abstract=2943164 or http://dx.doi.org/10.2139/ssrn.2943164

Vinicius Carrasco

Independent ( email )

No Address Available

Vitor Farinha Luz (Contact Author)

University of British Columbia ( email )

997-1873 East Mall
Vancouver, BC V6T 1Z1
Canada

Paulo Klinger Monteiro Sr.

Getulio Vargas Foundation (FGV) - EPGE ( email )

sala 1103
Rio de Janeiro RJ, 22250-900
Brazil
+55 21 37995838 (Phone)
+55 21 25538821 (Fax)

Humberto Moreira

Fundacao Getulio Vargas (FGV) ( email )

R. Dr. Neto de Araujo 320 cj 1307
Rio de Janeiro, Rio de Janeiro 22250-900
Brazil

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