Center for Algorithms, Data, and Market Design at Yale (CADMY)

We develop a mechanism design framework for AI agents whose alignment (preferences) and capabilities (feasible actions and information) are unknown. We want such agents to act on our behalf so mechanisms must incentivize both honesty and obedience. A one-sided imitation structure—capabilities can be concealed but not counterfeited—yields a revelation principle, a characterization of implementable policies via nested cyclical monotonicity, and conditions under which eliciting higher-order beliefs can discipline multiple agents. We apply our framework to stylized examples of (i) sandbagging in which a more capable agent pretends to be less capable; (ii) an alignment–interpretability trade-off, where the two are substitutes in the instrument but complements in value; (iii) discipline via peer scoring; (iv) coupling rewards to induce competition among multiple agents; and (v) scalable oversight and reward shaping.        

We study efficient dynamic mechanism design with independent private values when agents do not share a common prior over the stochastic environment. Each agent privately observes the kernel governing her own type evolution and may hold arbitrary beliefs about others’ kernels. We include kernels in agents’ type spaces and show that the dynamic team mechanism of Athey and Segal (2013) and the dynamic pivot mechanism of Bergemann and Välimäki (2010) implement the socially efficient allocation in periodic ex-post equilibrium. We further show that kernels need be elicited only at the outset and that these mechanisms induce the efficient private acquisition of kernels.

The optimal mechanism for selling a divisible good under convex production costs can be arbitrarily complex, yet firms overwhelmingly use two-part tariffs: a fixed fee plus a constant markup over production cost. We quantify the profit this simplicity sacrifices. For regular value distributions, a two-part tariff guarantees a fraction of the optimal profit that depends only on a lower bound m on the elasticity of the marginal cost, independent of the value distribution. The guarantee approaches 1 as m grows, and is impossible without such a bound. Beyond regularity, no two-part tariff guarantees a constant fraction, but a menu of K + 1 tariffs with a common markup does when the ironed virtual value has K ironing intervals; moreover, the menu size must scale with K. With multiple product lines, the better of separate sales and a single access fee granting purchases at production cost achieves a constant fraction of the optimal profit. These results provide a theoretical foundation for the ubiquity of simple cost-based pricing.

We study efficient dynamic mechanism design with independent private values when agents do not share a common prior over the stochastic environment. Each agent privately observes the stochastic kernel governing the evolution of her own type and may hold arbitrary beliefs about the kernels of others. We extend the agents’ type space to include the kernel itself and show that the dynamic team mechanism of Athey and Segal (2013) and the dynamic pivot mechanism of Bergemann and Välimäki (2010) implement the socially efficient allocation in periodic ex-post equilibrium. We further show that kernels can be elicited only once, at the outset, and that the same mechanisms induce the efficient private acquisition of the stochastic kernels.

We analyze a multidimensional screening model in which a principal offers a menu of quality-price pairs to a consumer with multiple dimensions of private information and a quasilinear utility function. We derive necessary conditions for optimality, and use them to provide insight into optimal exclusion, positive trade, and screening. We then recast the problem in terms of incremental quality levels and prices, the so-called demand-profile approach (DPA). Under DPA, the problem decouples across increments and can be solved one at a time. We provide novel conditions under which DPA recovers the solution to the full problem exactly or approximately, and which make the necessary conditions sufficient for optimality: essentially, valuations must be sufficiently correlated across quality increments. Applied to empirical estimates of demand for health insurance, we show that DPA is approximately valid, and we apply it to understand equilibrium outcomes in a monopoly insurance market.

We analyze consumer surplus when a monopolist can adjust both prices and prod-uct qualities across segments, engaging in second- and third-degree price discrimination simultaneously. We characterize the consumer-optimal segmentation and show that it has a striking structure: consumers with the same value receive the same quality in every segment, though prices differ. Under mild conditions, any segmentation harms consumers if and only if demand is sufficiently more elastic than supply. Hence, po-tential benefits for consumers depend critically on demand and supply elasticities. These findings have implications for regulatory policy regarding price discrimination and market segmentation.