Similarity Nash Equilibria in Statistical Games

Abstract

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. (JEL C72, C73)