Routing Game on the Line: The Case of Multi-players

  • Abdelillah Karouit
  • Majed Haddad
  • Eitan Altman
  • Moulay Abdellatif Lmater
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10542)


In this paper, we tackle the problem of a sequential routing game where multiple users coexist and competitively send their traffic to a destination over a line. The users arrive at time epoch with a given capacity. Then, they ship their demands over time on a shared resource. The state of players evolve according to whether they decide to transmit or not. The decision of each user is thus spatio-temporal control. We provide an explicit expression of the equilibrium of such systems and compare it to the global optimum case. In particular, we determine the expression of price of anarchy of such scheme and identify a Braess-type paradox in the context of sequential routing game.


Sequential routing game Nash equilibrium Price of anarchy Braess-type paradox 


  1. 1.
    Wardrop, J.G.: Some theoretical aspects of road traffic research communication networks. Proc. Inst. Civ. Eng. Part 2 1, 325–378 (1952)Google Scholar
  2. 2.
    Patriksson, M.: The Traffic Assignment Problem: Models and Methods. VSP, Utrecht (1994)Google Scholar
  3. 3.
    Orda, A., Rom, R., Shimkin, N.: Competitive routing in multi-user environments. IEEE/ACM Trans. Netw. 1, 510–521 (1993)CrossRefGoogle Scholar
  4. 4.
    Haurie, A., Marcotte, P.: On the relationship between Nash-Cournot and Wardrop equilibria. Networks 15, 295–308 (1985)CrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    Park, K., Sitharam, M., Chen, S.: Quality of service provision in noncooperative networks with diverse user requirements. Decis. Support Syst. 28(1–2), 101–122 (2000)CrossRefGoogle Scholar
  6. 6.
    Rosenthal, R.W.: A class of games possessing pure strategy Nash equilibria. Int. J. Game Theory 2, 65–67 (1973)CrossRefMATHMathSciNetGoogle Scholar
  7. 7.
    Haddad, M., Altman, E., Gaillard, J.: Sequential routing game on the line: transmit or relay? In: Proceeding of Communications and Information Technology (ICCIT), June 2012Google Scholar
  8. 8.
    Hanawal, M.K., Altman, E., El-Azouzi, R., Prabhu, B.J.: Spatio-temporal control for dynamic routing games. In: Proceedings of Game Theory for Networks (GameNets), Shanghai, China, April 2011Google Scholar
  9. 9.
    Altman, E., Basar, T., Jimenez, T., Shimkin, N.: Competitive routing in networks with polynomial cost. IEEE Trans. Autom. Control 47, 92–96 (2002)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Altman, E., Kuri, J., El-Azouzi, R.: A routing game in networks with lossy links. In: 7th International Conference on NETwork Games COntrol and OPtimization (NETGCOOP), Trento, Italy, October 2014Google Scholar
  11. 11.
    Kameda, H., Pourtallier, O.: Paradoxes in distributed decisions on optimal load balancing for networks of homogeneous computers. J. ACM 49(3), 407–433 (2002)CrossRefMATHMathSciNetGoogle Scholar
  12. 12.
    Wie, B.W., Friesz, T., Tobin, R.: Dynamic user optimal traffic assignment on congested multidestination networks. Transp. Res. 24B(6), 431–442 (1990)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Abdelillah Karouit
    • 1
  • Majed Haddad
    • 1
  • Eitan Altman
    • 2
  • Moulay Abdellatif Lmater
    • 3
  1. 1.LIA/CERI, University of Avignon, AgroparcAvignonFrance
  2. 2.INRIA Sophia AntipolisSophia AntipolisFrance
  3. 3.L-IR2M, Faculty of Sciences and TechniquesHassan 1st UniversitySettatMorocco

Personalised recommendations