Robust Mechanisms: The Curvature Case

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 non- linear 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 some conditions, distortions in the optimal mechanism are decreasing in types. This monotonicity has relevant consequences for several applications discussed. Our charac- terization 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 characteriza- tion 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.