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A differential game model of Nash equilibrium on a congested traffic network
Author(s) -
Wie ByungWook
Publication year - 1993
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/net.3230230606
Subject(s) - differential game , nash equilibrium , mathematical optimization , generalization , computer science , game theory , mathematical economics , traffic network , best response , traffic flow (computer networking) , time horizon , epsilon equilibrium , differential (mechanical device) , simple (philosophy) , flow network , mathematics , engineering , mathematical analysis , philosophy , computer security , epistemology , aerospace engineering
This paper considers the problem of the competition among a finite number of players who must transport the fixed volume of traffic on a simple network over a prescribed planning horizon. Each player attempts to minimize his total transportation cost by making simultaneous decisions of departure time, route, and flow rate over time. The problem is modeled as a N ‐person nonzero‐sum differential game. Two solution concepts are applied: [1] the open‐loop Nash equilibrium solution and [2] the feedback Nash equilibrium solution. Optimality conditions are derived and given an economic interpretation as a dynamic game theoretic generalization 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 systems. © 1993 by John Wiley & Sons, Inc.