The dynamic mixed behavior traffic network equilibrium model is formulated as a noncooperative N-person nonzero-sum differential game under the open-loop information structure. A simple network is considered where one origin–destination pair is connected by parallel arcs and two types of players – User Equilibrium (UE) and Cournot–Nash (C–N) – interact through the congestion phenomenon. Each of UE and C–N players attempts to achieve its own prescribed objective by making a continuum of simultaneous decisions of departure time, route, and departure flow rate over a fixed time interval. The necessary and sufficient conditions are derived and given economic interpretation as a dynamic game theoretic generalization of the mixed behavior traffic network equilibrium principle which requires equilibration of average costs for UE players and equilibration of marginal costs for C–N players. An approximate iterative algorithm is proposed for solving the model in discrete time, which makes use of the augmented Lagrangian method and the gradient method. A numerical example is presented and future extensions of the model and the algorithm are also discussed.
