A DIFFERENTIAL GAME MODEL OF NASH EQUILIBRIUM ON A CONGESTED TRAFFIC NETWORK

This paper considers the problem of the competition among a finite num ber of players who must transport the fixed volume of traffic on a sim ple network over a prescribed planning horizon. Each player attempts t o minimize his total transportation cost by making simultaneous decisi ons of departure time, route, and flow rate over time. The problem is modeled as a N-person nonzero-sum differential game. Two solution conc epts are applied: [1] the open-loop Nash equilibrium solution and [2] the feedback Nash equilibrium solution. Optimality conditions are deri ved and given an economic interpretation as a dynamic game theoretic g eneralization 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 sy stems. (C) 1993 by John Wiley & Sons, Inc.