Mechanism design without revenue equivalence

We study mechanism design problems in quasi-linear environments where the envelope theorem and revenue equivalence principle fail due to non-convex and non-differentiable valuations. We obtain a characterization of incentive compatibility based on the Mirrlees representation of the indirect utility and a monotonicity condition on the allocation rule, which pin down the range of possible payoffs as a function of the allocation rule. To illustrate our approach we derive the optimal selling mechanism in a buyer-seller situation where the buyer is loss-averse; we find a budget-balanced, efficient mechanism in a public goods location model; and we consider a principal-agent model with ex post non-contractible actions available to the agent.