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On the relationship between dynamic Nash and instantaneous user equilibria
Author(s) -
Wie ByungWook,
Tobin Roger L.
Publication year - 1998
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/(sici)1097-0037(199809)32:2<141::aid-net7>3.0.co;2-b
Subject(s) - nash equilibrium , epsilon equilibrium , best response , correlated equilibrium , differential game , mathematical optimization , mathematical economics , mathematics , repeated game , solution concept , equilibrium selection , generalization , computer science , game theory , mathematical analysis
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