A differential game model of Nash equilibrium on a congested traffic network

This paper considers the problem of the competition among a finite number of players who must transport the fixed volume of traffic on a simple network over a prescribed planning horizon. Each player attempts to minimize his total transportation cost by making simultaneous decisions of departure time, route, and flow rate over time. The problem is modeled as a N‐person nonzero‐sum differential game. Two solution concepts are applied: [1] the open‐loop Nash equilibrium solution and [2] the feedback Nash equilibrium solution. Optimality conditions are derived and given an economic interpretation as a dynamic game theoretic generalization of Wardrop's second principle. Future extensions of the model are also discussed. The model promises potential applications to Intelligent Vehicle Highway Systems (IVHS) and air traffic control systems.