  This paper examines the long-run behavior of learning with bandit feedback in
non-cooperative concave games. The bandit framework accounts for extremely
low-information environments where the agents may not even know they are
playing a game; as such, the agents' most sensible choice in this setting would
be to employ a no-regret learning algorithm. In general, this does not mean
that the players' behavior stabilizes in the long run: no-regret learning may
lead to cycles, even with perfect gradient information. However, if a standard
monotonicity condition is satisfied, our analysis shows that no-regret learning
based on mirror descent with bandit feedback converges to Nash equilibrium with
probability $1$. We also derive an upper bound for the convergence rate of the
process that nearly matches the best attainable rate for single-agent bandit
stochastic optimization.
