Screening while Controlling an Externality

We propose a tractable framework to introduce externalities in a screening model. Agents differ in both payoff-type and influence (how strongly their actions affect others). Applications range from pricing network goods to regulating industries that create externalities. Inefficiencies arise only if the payoff-type is unobservable. When both dimensions are unobserved, the optimal allocation satisfies lexicographic monotonicity: increasing along the payoff-type to satisfy incentive compatibility, but tilted towards influential agents to produce the externality. In particular, the allocation depends on a private characteristic that is payoff-irrelevant for the agent. We characterize the solution through a two-step ironing procedure that addresses the nonmonotonicity in virtual values arising from the countervailing impact of payoff-types and influence. If observable, influence is used as a signal of the payoff-type. We provide sufficient conditions for rents from influence to emerge even in a setting featuring atomistic agents.