Traffic Flow Analysis Dovetailed with Evolutionary Game Theory

  • Jun Tanimoto
Part of the Evolutionary Economics and Social Complexity Science book series (EESCS, volume 6)


In this chapter, we concern ourselves with traffic flow as another meaningful example of a situation in which evolutionary game theory can be applied. Although the study of traffic flow was originally thought to be best explained using fluid dynamics, a multi-agent simulation technique that has been widely used in the field of evolutionary games has been applied to the problem, under the name of cellular automaton (CA). In this chapter, we first explain how traffic flow can be modeled. Next, we discuss how evolutionary game theory can be applied to this traffic flow. One can consider the dynamics of traffic flow to be like a multi-player game, with vehicles being controlled by drivers who compete to access to a road as a finite resource in order to reduce their personal travel time. This implies that traffic flow may change its phase depending on traffic density, and that it entails a social dilemma that might also change its game class, depending on the density. We reveal that various social dilemmas are hidden behind different aspects of traffic flows, which may be considered remarkable. Traffic flow is a game committed by agents – drivers, which seems some sort of human drama unlike we naturally think that traffic flow is governed by rigid physics because the theory of fluid dynamics, one of the representative hard-core physics fields, has been applied to it.


Traffic Flow Social Dilemma Open Boundary Condition Evolutionary Game Theory Lane Change 


  1. Bando, M., K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama. 1994. Structure stability of congestion in traffic dynamics. Japan Journal of Industrial and Applied Mathematics 11: 203–223.MATHMathSciNetCrossRefGoogle Scholar
  2. Bando, M., K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama. 1995. Dynamical model of traffic congestion and numerical simulation. Physical Review E 51: 1035–1042.CrossRefADSGoogle Scholar
  3. Gao, K., R. Jiang, S.X. Hu, H. Wang, and Q.S. Wu. 2007. Cellular-automaton model with velocity adaptation in the framework of Kerners three-phase traffic theory. Physical Review E 76: 026105.CrossRefADSGoogle Scholar
  4. Gao, K., R. Jiang, B.H. Wang, and Q.S. Wu. 2009. Discontinuous transition from free flow to synchronized flow induced by short-range interaction between vehicles in a three-phase traffic flow mode. Physica A 388: 3233–3243.CrossRefADSGoogle Scholar
  5. Gazis, C., R. Herman, and R.W. Rothery. 1961. Nonlinear follow-the-leader models of traffic flow. Operations Research 9: 545–567.MATHMathSciNetCrossRefGoogle Scholar
  6. Helbing, D. 1995. Improved fluid-dynamic model for vehicular traffic. Physical Review E 51: 3164–3169.CrossRefADSGoogle Scholar
  7. Kerner, B.S. 2009. Introduction to modern traffic flow theory and control. Berlin: Springer.MATHCrossRefGoogle Scholar
  8. Kerner, B.S., and P. Konhäuser. 1994. Structure and parameters of clusters in traffic flow. Physical Review E 50: 54–83.CrossRefADSGoogle Scholar
  9. Kerner, B.S., H. Rehborn, R.-P. Schafer, S.L. Klenopv, J. Palmer, S. Lorkowski, and N. Witte. 2013. Traffic dynamics in empirical probe vehicle data studied with three-phase theory: Spatiotemporal reconstruction of traffic phases and generation of jam warning messages. Physica A 392: 221–251.CrossRefADSGoogle Scholar
  10. Knospe, W., L. Santen, A. Schadschneider, and M. Schreckenberg. 2000. Toward a realistic microscopic description of highway traffic. Journal of Physics A 33: L477–L485.MATHMathSciNetCrossRefADSGoogle Scholar
  11. Kokubo, S., J. Tanimoto, and A. Hagishima. 2011. A new Cellular Automata Model including a decelerating damping effect to reproduce Kerner’s three-phase theory. Physica A 390(4): 561–568.CrossRefADSGoogle Scholar
  12. Kukida, S., J. Tanimoto, and A. Hagishima. 2011. Analysis of the influence of lane changing on traffic-flow dynamics based on the cellular automaton model. International Journal of Modern Physics C 22(3): 271–281.CrossRefADSGoogle Scholar
  13. Lighthill, M.J., and G.B. Whitham. 1955. On kinematic waves. II. A theory of traffic flow on long crowded roads. Proceedings of the Royal Society of London Series A 229: 317–345.MATHMathSciNetCrossRefADSGoogle Scholar
  14. Nagel, K., and Schreckenberg, M. 1992. A cellular automaton model for freeway traffic. Journal de Physique France II:2221–2229.Google Scholar
  15. Nakata, M., A. Yamauchi, J. Tanimoto, and A. Hagishima. 2010. Dilemma game structure hidden in traffic flow at a bottleneck due to a 2 into 1 lane junction. Physica A 389: 5353–5361.CrossRefADSGoogle Scholar
  16. Neubert, L., L. Sante, A. Schadschneider, and M.L. Schreckenberg. 1999. Single-vehicle data of high traffic: A statistical analysis. Physical Review E 60: 6480.CrossRefADSGoogle Scholar
  17. Nishinari, K., and D. Takahashi. 1998. Analytical properties of ultradiscrete Burgers equation and rule-184 cellular automaton. Journal of Physics A: Mathematical and General 31: 5439–5450.MATHCrossRefADSGoogle Scholar
  18. Pipes, L.A. 1953. An operational analysis of traffic dynamics. Journal of Applied Physics 24: 274–281.MathSciNetCrossRefADSGoogle Scholar
  19. Sakai, S., K. Nishinari, and S. Iida. 2006. A new stochastic cellular automaton model on traffic flow and its jamming phase transition. Journal of Physics A: Mathematical and General 39: 15327–15339.MATHMathSciNetCrossRefGoogle Scholar
  20. Shigaki, K., J. Tanimoto, and A. Hagishima. 2011. A revised stochastic optimal velocity model considering the velocity Gap with a preceding vehicle. International Journal of Modern Physics C 22(9): 1005–1014.MATHCrossRefADSGoogle Scholar
  21. Wolfram, S. 1986. Theory and applications of cellular automata. Singapore: World Scientific.MATHGoogle Scholar
  22. Yamauchi, A., J. Tanimoto, A. Hagishima, and H. Sagara. 2009. Dilemma game structure observed in traffic flow at a 2-to-1 lane junction. Physical Review E 79: 036104.CrossRefADSGoogle Scholar

Copyright information

© Springer Japan 2015

Authors and Affiliations

  • Jun Tanimoto
    • 1
  1. 1.Graduate School of Engineering SciencesKyushu University InterdisciplinaryFukuokaJapan

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