  We study the notoriously difficult no-sensing adversarial multi-player
multi-armed bandits (MP-MAB) problem from a new perspective. Instead of
focusing on the hardness of multiple players, we introduce a new dimension of
hardness, called attackability. All adversaries can be categorized based on the
attackability and we introduce Adversary-Adaptive Collision-Communication
(A2C2), a family of algorithms with forced-collision communication among
players. Both attackability-aware and unaware settings are studied, and
information-theoretic tools of the Z-channel model and error-correction coding
are utilized to address the challenge of implicit communication without
collision information in an adversarial environment. For the more challenging
attackability-unaware problem, we propose a simple method to estimate the
attackability enabled by a novel error-detection repetition code and randomized
communication for synchronization. Theoretical analysis proves that asymptotic
attackability-dependent sublinear regret can be achieved, with or without
knowing the attackability. In particular, the asymptotic regret does not have
an exponential dependence on the number of players, revealing a fundamental
tradeoff between the two dimensions of hardness in this problem.
