Uncoupled Learning Rules for Seeking Equilibria in Repeated Plays: An Overview

In this note, we consider repeated play of a finite game using learning rules whose period-by-period behavior probabilities or empirical distributions converge to some notion of equilibria of the stage game. Our primary focus is on uncoupled and com-pletely uncoupled learning rules. While the former relies on players being aware of only their own payoff functions and able to monitor the action taken by the others, the latter assumes that players only know their own past realized payoffs. We highlight the border between possible and impossible results using these rules. We also overview several uncoupled and completely uncoupled learning rules, most of which leverage notions of regret as the solution concept to seek payoff-improving action profiles.