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 distributions as their induced distributions over posteriors. We show that every extreme point in the set of all...

Two firms produce substitute goods of unknown quality. At each stage the firms set prices and a consumer with private information and unit demand buys from one of the firms. Both firms and consumers see the entire history of prices and purchases. Will such markets aggregate information? Will the...

Bayesian experts with a common prior that are exposed to different types of evidence possibly make contradicting probabilistic forecasts. A policy maker who receives the forecasts must aggregate them in the best way possible. This is a challenge whenever the policy maker is not familiar with the...

We consider a multi-receiver Bayesian persuasion problem where an informed sender tries to persuade a group of receivers to adopt a certain product. The sender is allowed to commit to a signaling policy where she sends a private signal to every receiver. The utility of the sender is a function...

This paper provides a model of social learning where the order in which actions are taken is determined by an $m$-dimensional integer lattice rather than along a line as in the herding model. The observation structure is determined by a random network. Every agent links to each of his preceding...

Consider a setting where many individuals make predictions over the (unknown) state of nature based on signals they receive independently. An outside Bayesian observer, familiar with the common prior shared by the individuals, can aggregate this information and identify correctly the actual...

We study a delegation problem within a Bayesian persuasion framework with the aim of understanding the incentive design of representatives. We are doing so by adding a preplay stage to the standard Bayesian persuasion model in which the receiver is allowed to choose a representative in order to...

We study a canonical setting of learning in networks where initially agents receive conditionally i.i.d. signals about a binary state. The distribution according to which signals are drawn is called an information structure. Agents repeatedly communicate beliefs with their neighbors and update...