We study mechanism design for a sophisticated agent with non-expected utility (EU)
preferences. We show that the revelation principle holds if and only if all types are EU
maximizers: if at least one type is a non-EU maximizer, randomizing over dynamic
mechanisms generates a strictly larger set of implementable allocations than using static
mechanisms. Moreover, dynamic stochastic mechanisms can fully extract the private
information of any type who doesn’t have uniformly quasi-concave preferences without
providing that type any rent. Full-surplus extraction is possible in a broad variety of
non-EU environments, but impossible for types with concave preferences.