ON THE RELATIONSHIP BETWEEN DYNAMIC NASH AND INSTANTANEOUS USER EQUILIBRIA

The problem of a dynamic Nash equilibrium traffic assignment with sche dule delays on congested networks is formulated as an N-person nonzero -sum differential game in which each player represents an origin-desti nation pair. Optimality conditions are derived using a Nash equilibriu m solution concept in the open-loop strategy space and given the econo mic interpretation as a dynamic game theoretic generalization of Wardr op's second principle. It is demonstrated that an open-loop Nash equil ibrium solution converges to an instantaneous dynamic user equilibrium solution as the number of players for each origin-destination pair in creases to infinity. An iterative algorithm is developed to solve a di screte-time version of the differential game and is used to numericall y show the asymptotic behavior of open-loop Nash equilibrium solutions on a simple network. A Nash equilibrium solution is also analyzed on the 18-arc network. (C) 1998 John Wiley & Sons, Inc.