Game-Theoretic Approach for Modeling of Selfish and Group Routing

Authors

  • Alexander Yu. Krylatov Saint Petersburg State University
  • Victor V. Zakharov Saint Petersburg State University

Abstract

The development of methodological tools for modeling of traffic flow assignment is crucial issue since traffic conditions influence significantly on quality of life nowadays. Herewith no secret that the development of in-vehicle route guidance and information systems could impact significantly on route choice as soon as it is highly believed that they are able to reduce congestion in an urban traffic area. Networks' users join groups of drivers who rely on the same route guidance system. Therefore, present paper is devoted to discussing approaches for modeling selfish and group routing. Network performance is deeply associated with competition between users of networks. So, the emphasis in our discussion is placed on game-theoretic approaches for appropriate modeling.

Keywords:

traffic assignment problem, selfish routing, user equilibrium of Wardrop, group routing, Nash equilibrium, system optimum of Wardrop

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References

Altman, E., T. Basar, T. Jimenez and N. Shimkin (2002). Competitive routing in networks with polynomial costs. IEEE Transactions on automatic control, 47(1), 92–96.

Altman, E., R. Combes, Z. Altman and S. Sorin (2011). Routing games in the many players regime. Proceedings of the 5th International ICST Conference on Performance Evaluation Methodologies and Tools, 525–527.

Altman, E. and H. Kameda (2005). Equilibria for multiclass routing problems in multi-agent networks. Advances in Dynamic Games, 7, 343–367.

Beckmann, M. J., C.B. McGuire and C. B. Winsten (1956). Studies in the Economics of Transportation. Yale University Press: New Haven, CT.

Bonsall, P. (1992). The influence of route guidance advice on route choice in urban networks. Transportation. 19, 1–23.

Charnes, A. and W.W. Cooper (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.

Dafermos, S.C. (1971). An extended traffic assignment model with applications to two-way traffic. Transportation Science, 5, 366–389.

Dafermos, S.C. and F.T. Sparrow (1969). The traffic assignment problem for a general network. Journal of Research of the National Bureau of Standards, 73B, 91–118.

Devarajan, S. (1981). A note on network equilibrium and noncooperative games. Transportation Research, 15B, 421–426.

Fisk, C. S. (1984). Game theory and transportation systems modelling. Transportation Research, 18B, 301–313.

Gartner, N.H. (1980). Optimal traffic assignment with elastic demands: a review. Part I. Analysis framework. Transportation Science, 14(2), 174–191.

Haurie, A. and P. Marcotte (1985). On the relationship between Nash-Cournot and Wardrop equilibria. Networks, 15, 295–308.

Korilis, Y.A. and A.A. Lazar (1995). On the existence of equilibria in noncooperative optimal flow control. Journal of the Association for Computing Machinery, 42(3), 584–613.

Korilis, Y.A., A.A. Lazar and A. Orda (1995). Architecting noncooperative networks. IEEE J. Selected Areas Commun, 13, 1241–1251.

Krylatov, A.Y., V.V. Zakharov and I.G. Malygin (2016). Competitive Traffic Assignment in Road Networks. Transport and Telecommunication, 17(3), 212–221.

La, R. J. and V. Anantharam (1997). Optimal routing control: game theoretic approach. Proc. of the 36th IEEE Conference on Decision and Control, 2910–2915.

Nash, J. (1951). Non-cooperative games. Annals of Mathematics, 54, 286–295.

Orda, A., R. Rom and N. Shimkin (1993). Competitive routing in multiuser communication networks. IEEE/ACM Transactions on Networking, 1(5), 510–521.

Patriksson, M. (1994). The traffic assignment problem: models and methods. VSP Publishers: Utrecht, Netherlands.

Patriksson, M. (2015). The traffic assignment problem: models and methods. Dover Publications, Inc: N.Y., USA.

Rosenthal, R. W. (1973). The network equilibrium problem in integers. Networks, 3, 53–59.

Roughgarden, T. (2005). Selfish Routing and the Price of Anarchy. MIT Press.

Sheffi, Y. (1985). Urban transportation networks: equilibrium analysis with mathematical programming methods. Prentice-Hall, Inc: N.J., USA.

Wardrop, J.G. (1952). Some theoretical aspects of road traffic research. Proc. Institution of Civil Engineers, 2, 325–378.

Xie, J., N. Yu and X. Yang (2013). Quadratic approximation and convergence of some bush-based algorithms for the traffic assignment problem. Transportation research Part B, 56, 15–30.

Zakharov, V. and A. Krylatov (2016). Competitive routing of traffic flows by navigation providers. Automation and Remote Control, 77(1), 179–189.

Zheng, H. and S. Peeta (2014). Cost scaling based successive approximation algorithm for the traffic assignment problem. Transportation research Part B, 68, 17–30.

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Published

2022-04-17

How to Cite

Yu. Krylatov, A., & V. Zakharov, V. (2022). Game-Theoretic Approach for Modeling of Selfish and Group Routing. Contributions to Game Theory and Management, 10. Retrieved from https://gametheory.spbu.ru/article/view/13258

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