Monotonicity in direct revelation mechanisms

This paper studies a standard screening problem where the principalʹs allocation rule is multi-dimensional, and the agentʹs private information is a one-dimensional continuous variable. Under standard assumptions, that guarantee monotonicity of the allocation rule in one-dimensional mechanisms, it is shown that the optimal allocation will be non-monotonic in a (weakly) generic sense once the principal can use all screening variables. The paper further gives conditions on the modelʹs parameters that guarantee that non-monotonic allocation rules will be optimal.