Limits and Limitations of No-Regret Learning in Games

We study the limit behavior and performance of no-regret dynamics in general game theoretic settings. We design protocols that achieve both good regret and equilibration guarantees in general games. In terms of arbitrary no-regret dynamics we establish a strong equivalence between them and coarse correlated equilibria. We examine structured game settings where stronger properties can be established for no-regret dynamics and coarse correlated equilibria. In congestion games, as we decrease the size of agents, coarse correlated equilibria become closely concentrated around the unique equilibrium flow of the nonatomic game. Moreover, we compare best/worst case no-regret learning behavior to best/worst case Nash in small games. We study these ratios both analytically and experimentally. These ratios are small for 2 × 2 games, become unbounded for slightly larger games, and exhibit strong anticorrelation.