Limits and limitations of no-regret learning in games

Abstract

AbstractWe 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. We also establish a strong equivalence between them and coarse correlated equilibria (CCE). We examine structured game settings where stronger properties can be established for no-regret dynamics and CCE. In congestion games with non-atomic agents (each contributing a fraction of the flow), as we decrease the individual flow of agents, CCE become closely concentrated around the unique equilibrium flow of the non-atomic game. Moreover, we compare best/worst case no-regret learning behavior to best/worst case Nash equilibrium (NE) in small games. We prove analytical bounds on these inefficiency ratios for 2×2 games and unboundedness for larger games. Experimentally, we sample normal form games and compute their measures of inefficiency. We show that the ratio distribution has sharp decay, in the sense that most generated games have small ratios. They also exhibit strong anti-correlation between each other, that is games with large improvements from the best NE to the best CCE present small degradation from the worst NE to the worst CCE.