On the relationship between dynamic Nash and instantaneous user equilibria

Journal Article


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 discrete‐time version of the differential game and is used to numerically 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. © 1998 John Wiley & Sons, Inc. Networks 32: 141–163, 1998

Related Topics

Related Publications

Related Content

Site Footer


This website is provided by John Wiley & Sons Limited, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ (Company No: 00641132, VAT No: 376766987)

Published features on are checked for statistical accuracy by a panel from the European Network for Business and Industrial Statistics (ENBIS)   to whom Wiley and express their gratitude. This panel are: Ron Kenett, David Steinberg, Shirley Coleman, Irena Ograjenšek, Fabrizio Ruggeri, Rainer Göb, Philippe Castagliola, Xavier Tort-Martorell, Bart De Ketelaere, Antonio Pievatolo, Martina Vandebroek, Lance Mitchell, Gilbert Saporta, Helmut Waldl and Stelios Psarakis.