Much of the literature on the price of anarchy studies the quality of Nash equilibria. In this talk we will focus on learning outcomes. We study the quality of outcome of the natural multiplicative-weights learning algorithm in games. Games often have a wide variety of equilibria often with vastly differing social costs. We show that in most classes of games, learning outcomes are no worse than the price of anarchy. In fact, in some classes of games, this natural learning algorithm results in vastly better social welfare than predicted by the price of anarchy.
Joint work with Georgios Piliouras and Bobby Kleinberg.