Statistical Inference in Games

We consider statistical inference in games. Each player obtains a small random sample of other players' actions, uses statistical inference to estimate their actions, and chooses an optimal action based on the estimate. In a sampling equilibrium with statistical inference (SESI), the sample is drawn from the distribution of players' actions based on this process. We characterize the set of SESIs in large two-action games, and compare their predictions to those of Nash equilibrium, and for different sample sizes and statistical inference procedures. We then study applications to competitive markets, markets with network effects, monopoly pricing, and search and matching markets.