Mechanism and Network Design with Private Negative Externalities

A revenue-maximizing monopolist is selling a single indivisible good to buyers who face a loss if any of its rival buyers obtain it. The rivalry is modeled through a network, an arc between a pair of buyers indicates that a buyer considers another buyer its rival, and the magnitude of the loss is the private information of each buyer. This loss-exposure due to competitive considerations can be viewed as a negative externality. First, using a Myersonian approach we derive the monopolist’s optimal mechanism for any given network. Second, we show that revenues depend on the network structure. Thus, in applications where it is possible, the monopolist might consider designing not only the mechanism but also the network (if not fully, at least partially). Third, we provide and fully describe the solution to the monopolist’s market design problem; that is, the joint network and mechanism design problem. Specifically, despite the nonmonotone impact of additional competition on the monopolist’s revenues, we determine revenue-maximizing rivalry networks (which in turn induce optimal mechanisms) and show that they are independent of distributional assumptions on buyers’ independent private loss values, provided virtual values are bounded from zero. We achieve these results under different restrictions on the network structure and formation. When rivalry is symmetric, matchings are optimal (with at most one path on three vertices). Thus, a market with a fragmented network structure yields higher revenues for the monopolist than a market with a completely connected network structure. However, asymmetric competitive relationships among buyers generate higher revenues than symmetric ones. The optimal asymmetric networks are characterized by (i) every buyer having at least one rival and (ii) the existence of a buyer not considered a rival by anyone.