  We consider the non-stochastic version of the (cooperative) multi-player
multi-armed bandit problem. The model assumes no communication at all between
the players, and furthermore when two (or more) players select the same action
this results in a maximal loss. We prove the first $\sqrt{T}$-type regret
guarantee for this problem, under the feedback model where collisions are
announced to the colliding players. Such a bound was not known even for the
simpler stochastic version. We also prove the first sublinear guarantee for the
feedback model where collision information is not available, namely
$T^{1-\frac{1}{2m}}$ where $m$ is the number of players.
