We consider a group of strategic agents who must each repeatedly take one of two possible actions. They learn which of the two actions is preferable from initial private signals and by observing the actions of their neighbors in a social network.

We consider a large class of social learning models in which a group of agents face uncertainty regarding a state of the world, share the same utility function, observe private signals, and interact in a general dynamic setting. We introduce social learning equilibria, a static equilibrium concept that abstracts away from the details of the given extensive form, but nevertheless captures the corresponding asymptotic equilibrium behavior. We establish general conditions for agreement, herding, and information aggregation in equilibrium, highlighting a connection between agreement and information aggregation.

We study how long-lived rational agents learn from repeatedly observing a private signal and each others’ actions. With normal signals, a group of any size learns more slowly than just four agents who directly observe each others’ private signals in each period. Similar results apply to general signal structures. We identify rational groupthink—in which agents ignore their private signals and choose the same action for long periods of time—as the cause of this failure of information aggregation.

Private signals model noisy information about an unknown state. Although these signals are called "private," they may still carry information about each other. Our paper introduces the concept of private private signals, which contain information about the state but not about other signals. To achieve privacy, signal quality may need to be sacrificed. We study the informativeness of private private signals and characterize those that are optimal in the sense that they cannot be made more informative without violating privacy. We discuss implications for privacy in recommendation systems, information design, causal inference, and mechanism design.

Stochastic dominance is a crucial tool for the analysis of choice under risk. It is typically analyzed as a property of two gambles that are taken in isolation. We study how additional independent sources of risk (e.g., uninsurable labor risk, house price risk) can affect the ordering of gambles. We show that, perhaps surprisingly, background risk can be strong enough to render lotteries that are ranked by their expectation ranked in terms of first-order stochastic dominance. We extend our results to second-order stochastic dominance and show how they lead to a novel and elementary axiomatization of mean-variance preferences.

Social learning is the updating of beliefs based on observation of others. Such observation can lead to efficient aggregation of information, but also to inaccurate decisions, fragility of mass behaviors, and, in the case of information cascades, to complete blockage of learning. We review the theory of information cascades and social learning and discuss important themes, insights, and applications of this literature as it has developed over the last 30 years. We also highlight open questions and promising directions for further theoretical and empirical exploration.

We study the set of possible joint posterior belief distributions of a group of agents who share a common prior regarding a binary state and who observe some information structure. For two agents, we introduce a quantitative version of Aumann’s agreement theorem and show that it is equivalent to a characterization of feasible distributions from a 1995 work by Dawid and colleagues. For any number of agents, we characterize feasible distributions in terms of a “no-trade” condition. We use these characterizations to study information structures with independent posteriors. We also study persuasion problems with multiple receivers, exploring the extreme feasible distributions.

We study repeated independent Blackwell experiments; standard examples include drawing multiple samples from a population, or performing a measurement in different locations. In the baseline setting of a binary state of nature, we compare experiments in terms of their informativeness in large samples. Addressing a question due to Blackwell (1951), we show that generically an experiment is more informative than another in large samples if and only if it has higher Rényi divergences. We apply our analysis to the problem of measuring the degree of dissimilarity between distributions by means of divergences. A useful property of Rényi divergences is their additivity with respect to product distributions. Our characterization of Blackwell dominance in large samples implies that every additive divergence that satisfies the data processing inequality is an integral of Rényi divergences.