Combined Traffic Assignment Model with Game Theory

The classical Wardrop principle assumes that users minimize either individual travel cost or overall system cost. Unlike the pure Wardrop equilibrium, this study deals with the problem of user equilibrium traffic assignment with game theory. We present a Stackelberg game on the network in which the SO player is the leader and the Cournot-Nash and user equilibrium players are the followers. The Cournot-Nash and user equilibrium players select the route, which is given the SO player´s routing. In contrast, the SO player select the routes to minimize total system travel cost. Based on combined model, the traffic assignment method was discussed, and the VI and generalized Lagrange multiplier method was used to get the solution. A simple example is presented. The example result shows that the efficient of Stackelberg model is higher than that of the UE system or SO system.