Mechanism design without revenue equivalence

We characterize incentive compatible mechanisms in quasi-linear environments where the envelope theorem and revenue equivalence fail due to non-convex and non-differentiable valuations. Despite these obstacles, we obtain a characterization based on the familiar Mirrlees representation of the indirect utility and a monotonicity condition on the allocation rule. These conditions pin down the range of possible payoffs as a function solely of the allocation rule, thus providing a revenue inequality. We use our characterization in two economic applications where standard techniques based on revenue equivalence fail. We find a budget-balanced efficient mechanism in a public goods setting, and we characterize the optimal selling mechanism when the buyer has loss-averse preferences à la Kőszegi and Rabin (2006).