In recent years, multi-player multi-armed bandits (MP-MAB) have been extensively studied due to their wide applications in cognitive radio networks and Internet of Things systems. While most existing research on MP-MAB focuses on synchronized settings, real-world systems are often decentralized and asynchronous, where players may enter or leave the system at arbitrary times, and do not have a global clock. This decentralized asynchronous setting introduces two major challenges. First, without a global time, players cannot implicitly coordinate their actions through time, making it difficult to avoid collisions. Second, it is important to detect how many players are in the system, but doing so may cost a lot. In this paper, we address the challenges posed by such a fully asynchronous setting in a decentralized environment. We develop a novel algorithm in which players adaptively change between exploration and exploitation. During exploration, players uniformly pull their arms, reducing the probability of collisions and effectively mitigating the first challenge. Meanwhile, players continue pulling arms currently exploited by others with a small probability, enabling them to detect when a player has left, thereby addressing the second challenge. We prove that our algorithm achieves a regret of $\mathcal{O}(\sqrt{T \log T} + {\log T}/{Δ^2})$, where $Δ$ is the minimum expected reward gap between any two arms. To the best of our knowledge, this is the first efficient MP-MAB algorithm in the asynchronous and decentralized environment. Extensive experiments further validate the effectiveness and robustness of our algorithm, demonstrating its applicability to real-world scenarios.