Message interaction among neighborhood is necessary for unmanned aerial vehicles (UAVs) and Time Division Multiple Access is a feasible implementation by which each UAV broadcasts in one dedicated slot. However, the dynamic character requires the access process fast and the constrained energy limits the feedbacks during the process uninformative. Therefore, this article focuses on the slot access problem in UAV swarms. To be energy saving, a collision discovery method which is independent of valid information is designed to play the role of feedback. Furthermore, considering the decentralized structure, the slot access problem is formulated as a game model. To reach the Nash Equilibrium of the game fast, a synchronous and uncoupled learning algorithm is proposed to, in which all UAVs update simultaneously based on the information they obtain. The algorithm releases the requirement for a scheduler or a common control channel and is therefore applicable in UAV swarms. Simulation results verify the effectiveness of the proposed method and some investigations about the requirement for the number of slots are made.