Recently in-vehicle route guidance and information systems are rapidly developing. Such systems are expected to reduce congestion in an urban traffic area. This social benefit is believed to be reached by imposing the route choices on the network users that lead to the system optimum traffic assignment. However, guidance service could be offered by different competitive business companies. Then route choices of different mutually independent groups of users may reject traffic assignment from the system optimum state. In this paper, a game theoretic approach is shown to be very efficient to formalize competitive traffic assignment problem with various groups of users in the form of non-cooperative network game with the Nash equilibrium search. The relationships between the Wardrop’s system optimum associated with the traffic assignment problem and the Nash equilibrium associated with the competitive traffic assignment problem are investigated. Moreover, some related aspects of the Nash equilibrium and the Wardrop’s user equilibrium assignments are also discussed.
1. Altman, E., Basar, T., Jimenez, T., Shimkin, N. (2002) Competitive routing in networks with polynomial costs. IEEE Transactions on automatic control, 47(1), 92-96.
2. Altman, E., Combes, R., Altman, Z., Sorin, S. (2011) Routing games in the many players regime. In: Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools, pp. 525-527.
3. Altman, E., Kameda, H. (2005) Equilibria for multiclass routing problems in multi-agent networks. Advances in Dynamic Games, 7, 343- 367.
4. Beckmann, M.J., McGuire, C.B., Winsten, C.B. (1956) Studies in the Economics of Transportation. New Haven, CT: Yale University Press.
5. Bonsall, P. (1992) The influence of route guidance advice on route choice in urban networks. Transportation, 19, 1-23.
6. Charnes, A., Cooper, W.W. (1958) Extremal principles for simulating traffic flow in a network. Proceedings of the National Academy of Science of the United States of America, 44, 201-204.
7. Dafermos, S.C. (1971) An extended traffic assignment model with applications to two-way traffic. Transportation Science, 5, 366-389.
8. Dafermos, S.C., Sparrow, F.T. (1969) The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards, 73B, 91-118.
9. Devarajan, S. (1981) A note on network equilibrium and noncooperative games. Transportation Research, 15B, 421-426.
10. Fisk, C.S. (1984) Game theory and transportation systems modelling. Transportation Research, 18B, 301-313.
11. Gartner, N.H. (1980) Optimal traffic assignment with elastic demands: a review. Part I. Analysis framework. Transportation Science, 14(2), 174-191.
12. Haurie, A., Marcotte, P. (1985) On the relationship between Nash-Cournot and Wardrop equilibria. Networks, 15, 295-308.
13. Korilis, Y.A., Lazar, A.A. (1995) On the existence of equilibria in noncooperative optimal flow control. Journal of the Association for Computing Machinery, 42(3), 584-613.
14. Korilis, Y.A., Lazar, A.A., Orda, A. (1995) Architecting noncooperative networks. IEEE J. Selected Areas Commun., 13, 1241-1251.
15. La, R.J., Anantharam, V. (1997) Optimal routing control: game theoretic approach. In: Proc. of the 36th IEEE Conference on Decision and Control, 2910-2915.
16. Nash, J. (1951) Non-cooperative games. Annals of Mathematics, 54, 286-295.
17. Orda, A., Rom, R., Shimkin, N. (1993) Competitive routing in multiuser communication networks. IEEE/ACM Transactions on Networking, 1(5), 510-521.
18. Patriksson, M. (1994) The traffic assignment problem: models and methods. Utrecht, Netherlands: VSP Publishers.
19. Patriksson, M. (2015) The traffic assignment problem: models and methods. N.Y., USA: Dover Publications, Inc.
20. Rosenthal, R.W. (1973) The network equilibrium problem in integers. Networks, 3, 53-59.
21. Sheffi, Y. (1985) Urban transportation networks: equilibrium analysis with mathematical programming methods. N.J.: Prentice-Hall, Inc, Englewood Cliffs.
22. Wardrop, J.G. (1952) Some theoretical aspects of road traffic research. Proc. Institution of Civil Engineers, 2, 325-378.
23. Xie, J., Yu, N., Yang, X. (2013) Quadratic approximation and convergence of some bush-based algorithms for the traffic assignment problem. Transportation research Part B, 56, 15-30.
24. Zakharov, V., Krylatov, A. (2014) Equilibrium Assignments in Competitive and Cooperative Traffic Flow Routing. IFIP Advances in Information and Communication Technology, 434, 641-648.
25. Zakharov, V., Krylatov, A. (2016) Competitive routing of traffic flows by navigation providers. Automation and Remote Control, 77(1), 179-189.
26. Zheng, H., Peeta, S. (2014) Cost scaling based successive approximation algorithm for the traffic assignment problem. Transportation research Part B, 68, 17-30.