In recent decades, unmanned aerial vehicles (UAVs) have been widely adopted such as serving as flying base stations. Compared to traditional solutions, the deployment of UAV s is fast and low-cost. However, due to UAVs' limited energy capacity, efficiently utilizing UAV s' energy is a matter of concern. One solution is to use rechargeable UAV s, but the challenge of charging schedule comes in the wake of it. In this paper, this problem is modeled as a non-cooperative game where a UAV can choose a strategy in order to maximize its payoff. Also, we have proved that the proposed game is an exact potential game (EPG) which ensures a Nash equilibrium (NE) with best-response dynamics. Numerical results show that the proposed algorithm has a larger coverage ratio and is more flexible than other algorithms in most environments; hence, a better performance.