We propose a tractable framework to introduce externalities into a monopolist screening model. Agents differ both in their payoff type and their influence, i.e. how strongly their action affects the aggregate externality. Applications range from non-linear pricing of a network good, to taxation or subsidization of industries that produce externalities (e.g. pollution and human capital formation). When both dimensions are unobserved (full screening) the optimal allocation satisfies lexicographic monotonicity: within a payoff-type, the monopolist optimally tilts the allocation towards influential agents to increase the externality, while standard IC drives monotonicity across payoff-types. 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. The allocation is inefficient if and only if the payoff-type is unobservable. Only influence is observable, equilibrium utility can vary across the latter as it is used as a signal of the payoff-type. We provide sufficient conditions for (expected) rents from influence to emerge.
We study a decision-framing design problem: a principal faces an agent with frame-dependent preferences and designs an extensive form with a frame at each stage. This allows the principal to circumvent incentive compatibility constraints by inducing dynamically inconsistent choices of the sophisticated agent. We show that a vector of contracts can be implemented if and only if it can be implemented using a canonical extensive form, which has a simple high-low-high structure using only three stages and the two highest frames, and employs unchosen decoy contracts to deter deviations.
We then turn to the study of optimal contracts in the context of the classic monopolistic screening problem and establish the existence of a canonical optimal mechanism, even though our implementability result does not directly apply. In the presence of naive types, the principal can perfectly screen by cognitive type and extract full surplus from naifs.
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