This paper presents an approach for defining, solving, and implementing dynamic cooperative maneuver problems in autonomous driving applications. The formulation of these problems considers a set of cooperating cars as part of a multiagent system. A reinforcement learning technique is applied to find a suboptimal policy. The key role in the presented approach is a multiagent maneuvering environment that allows for the simulation of car-like agents within an obstacle-constrained space. Each of the agents is tasked with reaching an individual goal, defined as a specific location in space. The policy is determined during the reinforcement learning process to reach a predetermined goal position for each of the simulated cars. In the experiments, three road scenarios—zipper, bottleneck, and crossroads—were used. The trained policy has been successful in solving the cooperation problem in all scenarios and the positive effects of applying shared rewards between agents have been presented and studied. The results obtained in this work provide a window of opportunity for various automotive applications.