Countervailing incentives in allocation mechanisms with type-dependent externalities

I study an allocation mechanism of a single item in the presence of type-dependent externalities between bidders. The type-dependency introduces countervailing incentives and the allocation sometimes requires that types in an interior subset obtain their reservation utility. Furthermore, truth-telling requires the ex-ante allocation to satisfy a non-trivial monotonicity condition. I show that this problem is technically different from the one analyzed in related single agent settings. I provide a procedure to identify the main properties of the ex-post allocation. Typically, the solution does not entail a single reserve price. More specifically, each agent faces an allocation rule contingent on whether his and his rival's types fall below, in or above the (endogenously determined) subset of types that obtain their reservation utility.