Connected and automated technologies for vehicles pave the way for major changes in traffic control methodology. A decentralized control system based on a communication network using vehicle-to-vehicle communications and each vehicle’s on-board controller will be one of the predominant approaches to vehicle trajectory optimization when the deployment of connected and automated vehicles (CAVs) has advanced, because of its scalability and fault resistance compared to the centralized system. In this study, we propose a dynamic game-based vehicle trajectory optimization approach that can be utilized in a decentralized control system based on CAV technologies for merging segments, which is one of the bottlenecks of highways. Since the decentralized system is constructed by equal individual vehicles that decide their own optimal control in conflicting situations, we introduce a game-theory-based approach for obtaining a satisfactory result for those vehicles. Further, for achieving the optimal result at the end of the target segment, we employ a dynamic game to design the whole interrelated time-series trajectories of competing pairs of vehicles. To tackle the curse of dimensionality, we use an efficient method to enumerate the sets of combinations – a zero-suppressed binary decision diagram (ZDD) – and propose an algorithm that uses this ZDD to solve the dynamic game. The performance of the proposed approach is demonstrated via numerical experiments, and is compared to a static game-based model and an individual dynamic decision model. The results prove the effectiveness of the proposed approach—it induces efficiently adjusted behaviors of competing vehicles and enables merging success, especially in a situation where the initial gaps between vehicles are not enough for immediate lane change, which is achieved by the combined effect of the game-theoretic approach and the dynamic decision approach.