Extremal incentive compatible transfers

We characterize the boundaries of the set of transfers (extremal transfers) implementing a given allocation rule without imposing any assumptions on the agentʼs type space or utility function besides quasi-linearity. Exploiting the concept of extremal transfers allows us to obtain an exact characterization of the set of implementable allocation rules (the set of transfers is non-empty) and the set of allocation rules satisfying Revenue Equivalence (the extremal transfers coincide). We then show how the extremal transfers can be put to use in mechanism design problems where Revenue Equivalence does not hold.