We consider a decentralized stochastic multi-armed bandit problem with multiple players. Each player aims to maximize his/her own reward by pulling an arm. The arms give rewards based on i.i.d. stochastic Bernoulli distributions. Players are not aware about the probability distributions of the arms. At the end of each turn, the players inform their neighbors about the arm he/she pulled and the reward he/she got. Neighbors of players are determined according to an Erd{\H{o}}s-R{\'e}nyi graph with connectivity $\alpha$. This graph is reproduced in the beginning of every turn with the same connectivity. When more than one player choose the same arm in a turn, we assume that only one of the players who is randomly chosen gets the reward where the others get nothing. We first start by assuming players are not aware of the collision model and offer an asymptotically optimal algorithm for $\alpha = 1$ case. Then, we extend our prior work and offer an asymptotically optimal algorithm for any connectivity but zero, assuming players aware of the collision model. We also study the effect of $\alpha$, the degree of communication between players, empirically on the cumulative regret by comparing them with traditional multi-armed bandit algorithms.

研究了分散的随机多臂老虎机问题，在通过Erdős-Rényi图连接的多个玩家中，优化各自获得奖励的概率分布，推导了针对不同连接度的算法，利用累计遗憾值比较传统多臂老虎机算法和本研究。

一种渐近最优算法解决多人多臂老虎机问题