TD n. 642 2015

Paulo Monteiro, Vitor Farinha Luz, Vinicius Nascimento Carrasco, Humberto Moreira.

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