Nash equilibria for models of traffic flow.

Alberto Bressan
Pennsylvania State University

In connection with the Lighthill-Whitham model of traffic flow, let a cost function be given, depending on the departure time and on the arrival time of each driver.
Under natural assumptions, there exists a unique
globally optimal solution, minimizing the sum of the costs to all drivers. However, actual traffic patterns are better described by the Nash equilibrium solution, where no driver can lower his individual cost by changing his own departure time. The talk will focus on the existence and properties of this Nash solution. Various extensions an open problems will be discussed.

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