  Consider N cooperative but non-communicating players where each plays one out
of M arms for T turns. Players have different utilities for each arm,
representable as an NxM matrix. These utilities are unknown to the players. In
each turn players select an arm and receive a noisy observation of their
utility for it. However, if any other players selected the same arm that turn,
all colliding players will all receive zero utility due to the conflict. No
other communication or coordination between the players is possible. Our goal
is to design a distributed algorithm that learns the matching between players
and arms that achieves max-min fairness while minimizing the regret. We present
an algorithm and prove that it is regret optimal up to a $\log\log T$ factor.
This is the first max-min fairness multi-player bandit algorithm with (near)
order optimal regret.
