Extreme Points and First-Order Stochastic Dominance: Theory and Applications

We characterize the extreme points of first-order stochastic dominance (FOSD) intervals and show how these intervals are at the heart of many topics in economics. Using these extreme points, we characterize the distributions of posterior quantiles, leading to an analog of a classical result regarding the distributions of posterior means. We apply this analog to various subjects, including the psychology of judgement, political economy, and Bayesian persuasion. In addition, FOSD intervals provide a common structure to security design. We use the extreme points to unify and generalize seminal results in that literature when either adverse selection or moral hazard pertains.
Comment: 45 pages, 5 figures