  We consider two agents playing simultaneously the same stochastic three-armed
bandit problem. The two agents are cooperating but they cannot communicate. We
propose a strategy with no collisions at all between the players (with very
high probability), and with near-optimal regret $O(\sqrt{T \log(T)})$. We also
argue that the extra logarithmic term $\sqrt{\log(T)}$ should be necessary by
proving a lower bound for a full information variant of the problem.
