  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.
