No-Regret Learning in Bayesian Games
This work provides theoretical guarantees for learning algorithms in Bayesian games, which model scenarios with private information, but it is incremental as it builds directly on existing smoothness proofs.
The paper extends no-regret learning results from complete-information games to Bayesian games, showing that coarse correlated equilibria achieve near-optimal welfare and that no-regret dynamics converge to Bayesian coarse correlated equilibrium.
Recent price-of-anarchy analyses of games of complete information suggest that coarse correlated equilibria, which characterize outcomes resulting from no-regret learning dynamics, have near-optimal welfare. This work provides two main technical results that lift this conclusion to games of incomplete information, a.k.a., Bayesian games. First, near-optimal welfare in Bayesian games follows directly from the smoothness-based proof of near-optimal welfare in the same game when the private information is public. Second, no-regret learning dynamics converge to Bayesian coarse correlated equilibrium in these incomplete information games. These results are enabled by interpretation of a Bayesian game as a stochastic game of complete information.