  In this paper, we study the problem of fair multi-agent multi-arm bandit
learning when agents do not communicate with each other, except collision
information, provided to agents accessing the same arm simultaneously. We
provide an algorithm with regret $O\left(N^3 \log \frac{B}{\Delta} f(\log T)
\log T \right)$ (assuming bounded rewards, with unknown bound), where $f(t)$ is
any function diverging to infinity with $t$. This significantly improves
previous results which had the same upper bound on the regret of order
$O(f(\log T) \log T )$ but an exponential dependence on the number of agents.
The result is attained by using a distributed auction algorithm to learn the
sample-optimal matching and a novel order-statistics-based regret analysis.
Simulation results present the dependence of the regret on $\log T$.
