Recently in-vehicle route guidance and information systems are rapidly developing. Such systems are expected to reduce congestion in an urban traffic area. This social benefit is believed to be reached by imposing the route choices on the network users that lead to the system optimum traffic assignment. However, guidance service could be offered by different competitive business companies. Then route choices of different mutually independent groups of users may reject traffic assignment from the system optimum state. In this paper, a game theoretic approach is shown to be very efficient to formalize competitive traffic assignment problem with various groups of users in the form of non-cooperative network game with the Nash equilibrium search. The relationships between the Wardrop’s system optimum associated with the traffic assignment problem and the Nash equilibrium associated with the competitive traffic assignment problem are investigated. Moreover, some related aspects of the Nash equilibrium and the Wardrop’s user equilibrium assignments are also discussed.
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