We study a multiplayer stochastic multi-armed bandit problem in which players cannot communicate, and if two or more players pull the same arm, a collision occurs and the involved players receive zero reward. We consider the challenging heterogeneous setting, in which different arms may have different means for different players, and propose a new, efficient algorithm that combines the idea of leveraging forced collisions for implicit communication and that of performing matching eliminations. We give a finite-time analysis of our algorithm, bounding its regret by O((log T)^{1+\kappa}) for any fixed \kappa>0. If the optimal assignment of players to arms is unique, we further show that it attains the optimal O(log(T)) regret, solving an open question raised at NeurIPS 2018.