Monotonicity in Direct Revelation Mechanisms

Abstract

This paper studies a standard mechanism design problem where the principal's allocation rule is multi-dimensional, and the agent's 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 model's parameters that guarantee that non-monotonic allocation rules will be optimal. It is shown that either (1) a total surplus function with negative cross-partial derivatives, or (2) a marginal utility (with respect to information) for the agent with positive cross-partial derivatives, can generate optimal non-monotonic allocation rules.

Keywords: Multi-dimensional Allocation Rules, Mechanism Design, Monotonicity

JEL Classification: C70, D82