Optimal Allocation Mechanisms with Single-Dimensional Private Information∗

We study revenue-maximizing allocation mechanisms for multiple heterogeneous objects when buyers care about the entire allocation, and not just about the ones they obtain. Buyers’ payoff depends on their cost parameter and, possibly, on their competitors’ costs. Costs are independently distributed across buyers, and both the buyers and the seller are risk-neutral. The formulation allows for complements, substitutes and externalities. We identify a number of novel characteristics of revenue-maximizing mechanisms: First, we find that revenue-maximizing reserve prices depend on the bids of other buyers. Second, we find that when non-participation payoffs are type-dependent, revenue-maximizing auctions may sell too often, or they may even be ex-post efficient.