Lane change maneuvers are main causes of traffic turbulence at highway bottlenecks. We propose a dynamic game framework to derive the system optimum strategy for a network of cooperative vehicles interacting at a merging bottleneck. Cooperative vehicles on the highway mainline seek for optimal strategies (i.e., whether and when to perform courtesy lane change to facilitate the merging vehicle) to minimize their cost, while taking into account potential future interactions at the merging section while minimizing the distance traveled on the acceleration lane. An optimal strategy is found by minimizing the joint cost of all interacting vehicles while respecting behavioral and physical constraints. Numerical examples show the feasibility of the approach in capturing the nature of conflict and cooperation during the merging process, and demonstrate the benefits of sharing information and cooperative control for connected and automated vehicles.