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.

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.