In this paper, we introduce a novel approach for analyzing the behavior of a vehicle that is controlled by both a human driver and a cognitive and cooperative automation at the same time. In a situation where a dynamic and a static obstacle force the driver-vehicle system to engage in a lane changing maneuver at a sooner or later point in time, the objective is to maximize the driving comfort, minimize risks, and, ultimately, avoid a crash with either obstacle. Hereby, the dynamic obstacle is another driver-vehicle system with similar properties as the first one. Therefore, their interaction can be modeled as a sequential game with imperfect information, since neither can perfectly predict the behavior of the other. As a proxy for comfort and safety, we use the time to collision (TTC) and compare it to the preferred TTC of each system. A further component of the utility function is the velocity, which serves to evaluate the time consumed to perform a maneuver as well as the costs related to it. Each system puts different weights on the individual components and, therefore, chooses different actions at different points in time. It can influence the velocity as well as the lane on which to drive. Using a simulation, we evaluate the behavior of both systems at several points in time until the static obstacle is passed.