Nash Equlibria for a Model of Traffic Flow
Speaker: Alberto Bressan, Penn State University
Location: Warren Weaver Hall 1302
Date: Thursday, April 26, 2012, 11 a.m.
In connection with the Lighthill-Whitham model of traffic flow, a cost functional can be introduced 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. Extensions to the case of several groups of drivers on a network of roads will also be discussed, together with open problems.