Uncertainity in Mechanism Design ∗

We consider a simple mechanism design problem with private values in which each agent perceives Knightian uncertainty over his opponents’ types. Uncertainty is formalized using incomplete preferences as in Bewley (1986). We show that the seller can extract all gains from trade with a direct mechanism in which truth-telling is a Nash equilibrium, in the sense that no buyer has a unilateral incentive to misrepresent his type. In a Nash equilibrium, however, truth-telling and mirepresenting can be incomparable alternatives. Thus we also consider an equilibrium concept in which truth-telling is optimal, that is, (weakly) preferred to other alternatives. In this case the full extraction of all gains from trade is feasible only if there is sufficient disagreement in beliefs. Otherwise, Vickrey mechanisms maximize the seller’s expected revenue. JEL Codes: D0, D5, D8, G1