Since network data commonly consists of observations from a single large network, researchers often partition the network into clusters in order to apply cluster‐robust inference methods. Existing such methods require clusters to be asymptotically independent. Under mild conditions, we prove that, for this requirement to hold for network‐dependent data, it is necessary and sufficient that clusters have low conductance, the ratio of edge boundary size to volume. This yields a simple measure of cluster quality. We find in simulations that when clusters have low conductance, cluster‐robust methods control size better than HAC estimators. However, for important classes of networks lacking low‐conductance clusters, the former can exhibit substantial size distortion. To determine the number of low‐conductance clusters and construct them, we draw on results in spectral graph theory that connect conductance to the spectrum of the graph Laplacian. Based on these results, we propose to use the spectrum to determine the number of low‐conductance clusters and spectral clustering to construct them.

We investigate the ability of a platform to design its marketplace to promote competition, improve consumer surplus, and increase its own payoff. We consider demand‐steering rules that reward firms that cut prices with additional exposure to consumers. We examine the impact of these rules both in theory and by using simulations with artificial intelligence pricing algorithms (specifically Q‐learning algorithms, which are commonly used in computer science). Our theoretical results indicate that these policies (which require little information to implement) can have strongly beneficial effects, even when sellers are infinitely patient and seek to collude. Similarly, our simulations suggest that platform design can benefit consumers and the platform, but that achieving these gains may require policies that condition on past behavior and treat sellers in a nonneutral fashion. These more sophisticated policies disrupt the ability of algorithms to rotate demand and split industry profits, leading to low prices.