Monotone Function Intervals: Theory and Applications

TL;DR

This paper studies monotone function intervals, characterizes their extreme points, and applies these findings to economic models involving information design, security, and judgment, unifying several key results in the field.

Contribution

It provides a novel characterization of extreme points of monotone function intervals and applies this to unify and extend results in economic information design and security models.

Findings

Characterization of extreme points of monotone function intervals

Application to posterior quantile distributions in economic settings

Unified framework for security design under adverse selection and moral hazard

Abstract

A monotone function interval is the set of monotone functions that lie pointwise between two fixed monotone functions. We characterize the set of extreme points of monotone function intervals and apply this to a number of economic settings. First, we leverage the main result to characterize the set of distributions of posterior quantiles that can be induced by a signal, with applications to political economy, Bayesian persuasion, and the psychology of judgment. Second, we combine our characterization with properties of convex optimization problems to unify and generalize seminal results in the literature on security design under adverse selection and moral hazard.