Nash Equilibrium in a Road Network with Many Groups of Users

In this chapter concentrates on the relationships between individual and group behaviour of drivers in a road network. Such relationships are established by comparing the optimal routing of drivers (system optimum of Wardrop), the competitive drivers’ groups routing (Nash equilibrium), and the selfish drivers routing (user equilibrium of Wardrop). Thus, the boundary conditions for traffic assignment in a road network were recently obtained for the first time. Wide analytical discussion on the topic as well as a survey of relevant references are presented. Moreover, a new behavioural model of traffic assignment in case of simultaneous selfish and group behaviour of drivers in a road network is formulated in the last section. An explicit solution to a behavioural traffic assignment problem is offered for a single-commodity linear network with non-interfering routes.

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