Uncertainty in Mechanism Design∗

We consider mechanism design problems in which agents perceive Knightian uncertainty. Uncertainty is formalized using incomplete preferences, as in Bewley (1986). Without completeness, individual decision making depends on a set of beliefs, and an action is preferred to another if and only if it has larger expected utility for all beliefs in this set. We consider two natural notions of incentive compatibility in this setting: maximal incentive compatibility requires that no strategy has larger expected utility than truth-telling for all beliefs, while optimal incentive compatibility requires that truth-telling has larger expected utility than all other strategies for all beliefs. In a model with a continuum of types, we show that optimal incentive compatibility is equivalent to ex-post incentive compatibility under fairly general conditions on beliefs. In a model with a discrete type space, we characterize full extraction of rents from private information. We show that full extraction requires sufficient disagreement in beliefs across types for optimal incentive compatible mechanisms. Contrary to the standard Bayesian case, we show that full extraction in optimal incentive compatible mechanisms is not generically possible. JEL Codes: D0, D5, D8, G1