Unmanned aerial vehicles (UAVs) are capable of serving as aerial base stations (BSs) for providing both cost-effective and on-demand wireless communications. This article investigates dynamic resource allocation of multiple UAVs enabled communication networks with the goal of maximizing long-term rewards. More particularly, each UAV communicates with a ground user by automatically selecting its communicating users, power levels and subchannels without any information exchange among UAVs. To model the uncertainty of environments, we formulate the long-term resource allocation problem as a stochastic game for maximizing the expected rewards, where each UAV becomes a learning agent and each resource allocation solution corresponds to an action taken by the UAVs. Afterwards, we develop a multi-agent reinforcement learning (MARL) framework that each agent discovers its best strategy according to its local observations using learning. More specifically, we propose an agent-independent method, for which all agents conduct a decision algorithm independently but share a common structure based on Q-learning. Finally, simulation results reveal that: 1) appropriate parameters for exploitation and exploration are capable of enhancing the performance of the proposed MARL based resource allocation algorithm; 2) the proposed MARL algorithm provides acceptable performance compared to the case with complete information exchanges among UAVs. By doing so, it strikes a good tradeoff between performance gains and information exchange overheads.