In this paper, we present a unifying framework for analyzing equilibria and designing interventions for large network games sampled from a stochastic network formation process represented by a graphon. To this end, we introduce a new class of infinite population games, termed graphon games , in which a continuum of heterogeneous agents interact according to a graphon, and we show that equilibria of graphon games can be used to approximate equilibria of large network games sampled from the graphon. This suggests a new approach for design of interventions and parameter inference based on the limiting infinite population graphon game. We show that, under some regularity assumptions, such approach enables the design of asymptotically optimal interventions via the solution of an optimization problem with much lower dimension than the one based on the entire network structure. We illustrate our framework on a synthetic data set and show that the graphon intervention can be computed efficiently and based solely on aggregated relational data.

Using a multisector general equilibrium model, we show that the interplay of idiosyncratic microeconomic shocks and sectoral heterogeneity results in systematic departures in the likelihood of large economic downturns relative to what is implied by the normal distribution. Such departures can emerge even though GDP fluctuations are approximately normally distributed away from the tails, highlighting the different nature of large economic downturns from regular business-cycle fluctuations. We further demonstrate the special role of input-output linkages in generating tail comovements, whereby large recessions involve not only significant GDP contractions, but also large simultaneous declines across a wide range of industries.

We present a model where social media platforms offer plans that intermix entertaining content with digital advertising (“ads”). Users derive utility from entertainment and learn about their valuation for a product from ads. While some users are fully rational, others naïvely perceive digital ads as more informative than they actually are. We characterize the profit-maximizing business model of the platform and show that welfare is lower when the platform monetizes through advertising instead of subscription both for naïfs (because they are targeted by intense digital advertising, which makes them over-optimistic about product quality and over-purchase the product) and for sophisticates (because the inflated demand from naïfs increases the firm’s price). This negative welfare effect is intensified when the platform can offer mixed business models that separate the naïve and sophisticated users into different plans. Our results are robust to firm-level and platform-level competition, because digital ads soften competition between both firms and platforms. We also show how digital ad taxes can improve welfare.<br><br>Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at <a href="http://www.nber.org/papers/w33017" TARGET="_blank">www.nber.org</a>.<br>

This paper develops a model of Bayesian learning from online reviews and investigates the conditions for learning the quality of a product and the speed of learning under different rating systems. A rating system provides information about reviews left by previous customers. observe the ratings of a product and decide whether to purchase and review it. We study learning dynamics under two classes of rating systems: full history , where customers see the full history of reviews, and summary statistics , where the platform reports some summary statistics of past reviews. In both cases, learning dynamics are complicated by a selection effect —the types of users who purchase the good, and thus their overall satisfaction and reviews depend on the information available at the time of purchase. We provide conditions for complete learning and characterize and compare its speed under full history and summary statistics. We also show that providing more information does not always lead to faster learning, but strictly finer rating systems do.