Social Learning through Statistics
I study a sequential social learning model in a general information environment. Each agent learns about an underlying state of the world by observing a state-signal directly about the state, which is unboundedly informative as in Smith and Sorensen (2000), and a summary statistic about other agents' actions and then chooses his own action. I introduce the concept of "normal statistics" and show that dispersed private information successfully aggregates in the long run under all normal statistics, provided that past statistics are public information for all subsequent agents. In general, when past statistics are not necessarily observed by subsequent agents, I introduce the concept of "weakly-separating statistics" which characterizes when information aggregation occurs.
Informational Intermediary: Unintended Welfare Loss and Market Stagnation, with Kai Hao Yang
This paper studies the impact of information intermediation on market outcomes. We consider a dynamic game in discrete time. In each period, a short-lived producer sets the price of a product and sells it to consumers through a long-lived information intermediary; the intermediary observes the price and designs the information structure of consumers' signals about the product; then, short-lived consumers observe their signals and decide whether to purchase the product. The intermediary earns a fixed percentage of the sales revenue and can grow its consumer base over time by serving consumers well. We characterize the set of Markov perfect equilibria and show that, due to the strategic interaction between the producers and the intermediary, information intermediation may cause a Pareto inferior outcome with market stagnation, despite the intermediary's objective to maximize a weighted social welfare. We also characterize the set of subgame perfect equilibrium payoffs.
This paper studies the optimal design of a platform to incentivize its users to collectively acquire costly information about the quality of a product (or a service, an investment opportunity, etc.). Users arrive in discrete time. Each user observes information disclosed by the platform and may acquire a costly private signal about the product quality before making his purchase decision. The platform observes users past purchase history and can disclose any information about past histories to subsequent users. It is shown that if the information environment features negative feedback, it is optimal for the platform to release no information early on to induce user exploration, and publish a list of potentially good products at a later point in time, once and for all. On the other hand, if the information environment features positive feedback, it is optimal for the platform to continuously flag projects that are potentially good for an extended period of time right after the product is released. Welfare comparison with different benchmarks are discussed.
The efficiency of market economies and democratic political system depends on the accuracy of individuals’ beliefs. However, centralized information control has, from time to time, hindered efficient societal information aggregation. In this paper, we study to what extent information aggregation in social learning environments is affected by centralized information control of a principal with a state-independent preference. We consider a population of agents who arrive sequentially and obtain information about the state of the world both from their private signals and by observing information about other agents’ actions either exogenously or through the principal. Contrary to the naïve intuition, information aggregation can be very resilient, rather than fragile, provided that the agents have access to some minimal amount of “expanding” observations of others’ actions that are outside of the principal’s control. In general, the learning outcome depends on whether and how the beliefs generated by the private signals are bounded, as well as the type of exogenous observations that agents have.