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Speaker: Alberto Bressan
        Eberly Chair Professor
        Department of Mathematics
        Penn State University

TITLE:  Optima and equilibria for a model of traffic flow.

ABSTRACT:  In connection with the Lighthill-Whitham model of traffic flow, a cost functional will be considered, 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 total cost to all drivers. In a realistic situation, however, the actual traffic is better described by the Nash equilibrium solution, where no driver can lower his individual cost by changing his own departure time. A characterization of the Nash solution can be provided,  establishing its existence and  uniqueness. The costs of the optimal and of the equilibrium solution can be compared, for some specific examples. Various extensions and open problems will be discussed.