On the relationship between dynamic Nash and instantaneous user equilibria

✍ Scribed by Wie, Byung-Wook; Tobin, Roger L.

• Publisher: John Wiley and Sons
• Year: 1998
• Tongue: English
• Weight: 378 KB
• Volume: 32
• Category: Article
• ISSN: 0028-3045
• DOI: 10.1002/(sici)1097-0037(199809)32:2<141::aid-net7>3.0.co;2-b

✦ Synopsis

The problem of a dynamic Nash equilibrium traffic assignment with schedule delays on congested networks is formulated as an N-person nonzero-sum differential game in which each player represents an origin-destination pair. Optimality conditions are derived using a Nash equilibrium solution concept in the open-loop strategy space and given the economic interpretation as a dynamic game theoretic generalization of Wardrop's second principle. It is demonstrated that an open-loop Nash equilibrium solution converges to an instantaneous dynamic user equilibrium solution as the number of players for each origin-destination pair increases to infinity. An iterative algorithm is developed to solve a discretetime version of the differential game and is used to numerically show the asymptotic behavior of openloop Nash equilibrium solutions on a simple network. A Nash equilibrium solution is also analyzed on the 18-arc network.