  Multi-player Multi-Armed Bandits (MAB) have been extensively studied in the
literature, motivated by applications to Cognitive Radio systems. Driven by
such applications as well, we motivate the introduction of several levels of
feedback for multi-player MAB algorithms. Most existing work assume that
sensing information is available to the algorithm. Under this assumption, we
improve the state-of-the-art lower bound for the regret of any decentralized
algorithms and introduce two algorithms, RandTopM and MCTopM, that are shown to
empirically outperform existing algorithms. Moreover, we provide strong
theoretical guarantees for these algorithms, including a notion of asymptotic
optimality in terms of the number of selections of bad arms. We then introduce
a promising heuristic, called Selfish, that can operate without sensing
information, which is crucial for emerging applications to Internet of Things
networks. We investigate the empirical performance of this algorithm and
provide some first theoretical elements for the understanding of its behavior.
