We develop a tool akin to the revelation principle for dynamic mechanism‐selection games in which the designer can only commit to short‐term mechanisms. We identify a canonical class of mechanisms rich enough to replicate the outcomes of any equilibrium in a mechanism‐selection game between an uninformed designer and a privately informed agent. A cornerstone of our methodology is the idea that a mechanism should encode not only the rules that determine the allocation, but also the information the designer obtains from the interaction with the agent. Therefore, how much the designer learns, which is the key tension in design with limited commitment, becomes an explicit part of the design. Our result simplifies the search for the designer‐optimal outcome by reducing the agent's behavior to a series of participation, truth telling, and Bayes' plausibility constraints the mechanisms must satisfy.

We study games of incomplete information as both the information structure and the extensive form vary. An analyst may know the payoff‐relevant data but not the players' private information, nor the extensive form that governs their play. Alternatively, a designer may be able to build a mechanism from these ingredients. We characterize all outcomes that can arise in an equilibrium of some extensive form with some information structure. We show how to specialize our main concept to capture the additional restrictions implied by extensive‐form refinements.

Information policies such as scores, ratings, and recommendations are increasingly shaping society’s choices in high-stakes domains. We provide a framework to study the welfare implications of information policies on a population of heterogeneous individuals. We define and characterize the Bayes welfare set, consisting of the population’s utility profiles that are feasible under some information policy. The Pareto frontier of this set can be recovered by a series of standard Bayesian persuasion problems. We provide necessary and sufficient conditions under which an information policy exists that Pareto dominates the no-information policy. We illustrate our results with applications to data leakage, price discrimination, and credit ratings.

We recover valuations of time using detailed data from a large ride‐hail platform, where drivers bid on trips and consumers choose between a set of rides with different prices and wait times. Leveraging a consumer panel, we estimate demand as a function of both prices and wait times and use the resulting estimates to recover heterogeneity in the value of time across consumers. We study the welfare implications of personalized pricing and its effect on the platform, drivers, and consumers. Taking into account drivers' optimal reaction to the platform's pricing policy, personalized pricing lowers consumer surplus by 2.5% and increases overall surplus by 5.2%. Like the platform, drivers benefit from personalized pricing. By conditioning prices on drivers' wait times and not on consumers' data, the platform can capture a significant portion of the profits garnered from personalized pricing, and simultaneously benefit consumers.