One of the major challenges in optimization-based control of large-scale intelligent infrastructural networks such as traffic networks is to find efficient multilevel optimization schemes through which decisions can be made by agents or controllers of different interacting layers. The hierarchical game on which this dissertation is focused can be used to model this interaction. In particular, the so-called reverse Stackelberg game is considered, in which players act sequentially. Moreover, a leader player in this game proposes a leader function to the followers, which maps a follower's decision space to the leader's decision space. The leader thus influences a follower by making her decision dependent on a follower's decision, aiming to obtain the desired values of the decision variables. An example of such a function is by proposing monetary incentives associated with different routes in a traffic network, under the objective to induce the drivers to adopt those routes that lead to a system-optimal traffic distribution. The contributions described in this dissertation can be summarized as the development of existence conditions and solution methods for the general reverse Stackelberg game and the application of the game in order to mitigate traffic problems like congestion and vehicular emissions.