Similarity Nash Equilibria in Statistical Games

A statistical game is a game in which strategic interaction is mediated via a binary outcome y, coupled with a prediction problem where a characteristic x of the game may be used to predict its outcome y based on past values of (x,y). In Similarity Nash Equilibria, players combine statistical and strategic reasoning, using an estimate of y as a coordination device. They predict y by its similarity-weighted frequency and learn the optimal notion of similarity from the data. We prove that the model captures the importance of precedents and the endogenous formation of sunspots.