Information Design for Many Parameters
Thành Nguyen, Rakesh Vohra · 2025
A stochastic mapping from states to signals induces a distribution over possible posteriors. For a variety of purposes one is interested in parameters of these posteriors, possibly multi-dimensional, such as their quartiles or whether they first-order stochastically dominate some given distribution. Many parameters of interest can be encoded by requiring the posterior at each signal lie point-wise between two given distributions. Given a collection of these bounding pairs, one for each signal, we characterize the set of posteriors that can be realized by some stochastic mapping of states to signals. We provide applications of this result to, among others, the design of securities, price, and statistical discrimination.