Mean‐preserving contractions are critical for studying Bayesian models of information
design. We introduce the class of bi‐pooling policies, and the class of bi‐pooling …

An information designer has precise information about consumers' preferences over
products sold by oligopolists. The designer chooses what information to reveal to …

We consider a Bayesian persuasion problem where a sender's utility depends only on the
expected state. We show that upper censorship that pools the states above a cutoff and …

We present a unified duality approach to Bayesian persuasion. The optimal dual variable,
interpreted as a price function on the state space, is shown to be a supergradient of the …

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 …

We study the optimal design of fraud-proof allocation mechanisms without transfers. An
agent's eligibility relies on a score reflecting social value, but gaming generates …

We study the problem of a partisan gerrymanderer who assigns voters to equipopulous
districts so as to maximize his party's expected seat share. The designer faces both …

Should regulators reveal the models they use to stress‐test banks? In our setting, revealing
leads to gaming, but secrecy can induce banks to underinvest in socially desirable assets for …

A sender sells an object of unknown quality to a receiver who pays his expected value for it.
Sender and receiver might hold different priors over quality. The sender commits to a …

We consider a model of Bayesian persuasion with one informed sender and several
uninformed receivers. The sender can affect receivers' beliefs via private signals, and the …