Skip to main content
SpringerLink
Log in

Distributed Learning of Wardrop Equilibria

  • Conference paper
Book cover Unconventional Computing (UC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5204))

Included in the following conference series:

Abstract

We consider the problem of learning equilibria in a well known game theoretic traffic model due to Wardrop. We consider a distributed learning algorithm that we prove to converge to equilibria. The proof of convergence is based on a differential equation governing the global macroscopic evolution of the system, inferred from the local microscopic evolutions of agents. We prove that the differential equation converges with the help of Lyapunov techniques.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 74.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 99.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Altman, E., Hayel, Y., Kameda, H.: Evolutionary Dynamics and Potential Games in Non-Cooperative Routing. In: Wireless Networks: Communication, Cooperation and Competition (WNC3 2007) (2007)

    Google Scholar 

  2. Berenbrink, P., Friedetzky, T., Goldberg, L.A., Goldberg, P., Hu, Z., Martin, R.: Distributed Selfish Load Balancing. In: SODA 2006: Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm, pp. 354–363. ACM, New York (2006)

    Chapter  Google Scholar 

  3. Bournez, O.: Modèles Continus. Calculs. Algorithmique Distribuée. Hdr, Institut National Polytechnique de Lorraine (Décember 7, 2006)

    Google Scholar 

  4. Bournez, O., Campagnolo, M.L.: A Survey on Continuous Time Computations. In: New Computational Paradigms. Changing Conceptions of What is Computable, pp. 383–423. Springer, New York (2008)

    Google Scholar 

  5. Bournez, O., Campagnolo, M.L., Graça, D.S., Hainry, E.: Polynomial Differential Equations Compute All Real Computable Functions on Computable Compact Intervals. Journal of Complexity 23(3), 317–335 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Bournez, O., Hainry, E.: Recursive Analysis Characterized as a Class of Real Recursive Functions. Fundinform 74(4), 409–433 (2006)

    MATH  MathSciNet  Google Scholar 

  7. Cole, R., Dodis, Y., Roughgarden, T.: Low much can taxes help selfish routing? In: Proceedings of the 4th ACM Conference on Electronic Commerce (EC 2003), pp. 98–107. ACM Press, New York (2003)

    Chapter  Google Scholar 

  8. Cominetti, R., Correa, J.R., Stier-Moses, N.E.: Network Games with Atomic Players. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 525–536. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  9. Demailly, J.-P.: Analyse Numérique et Equations Différentielles. Presses Universitaires de Grenoble (1991)

    Google Scholar 

  10. Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence Time to Nash Equilibria. In: 30th International Conference on Automata, Languages and Programming (ICALP), pp. 502–513 (2003)

    Google Scholar 

  11. Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence Time to Nash equilibrium in Load Balancing. ACM Transactions on Algorithms 3(3) (2007)

    Google Scholar 

  12. Even-Dar, E., Mansour, Y.: Fast Convergence of Selfish Rerouting. In: SODA 2005: Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms. Society for Industrial and Applied Mathematics, pp. 772–781 (2005)

    Google Scholar 

  13. Fischer, S., Räcke, H., Vöcking, B.: Fast Convergence to Wardrop Equilibria by Adaptive Sampling Methods. In: Proceedings of the thirty-eighth annual ACM symposium on Theory of computing, pp. 653–662 (2006)

    Google Scholar 

  14. Fischer, S., Vocking, B.: On the Evolution of Selfish Routing. In: Albers, S., Radzik, T. (eds.) ESA 2004. LNCS, vol. 3221. Springer, Heidelberg (2004)

    Google Scholar 

  15. Fischer, S., Vöcking, B.: Adaptive Routing with Stale Information. In: Proceedings of the twenty-fourth annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing, pp. 276–283 (2005)

    Google Scholar 

  16. Fleischer, L.: Linear Tolls Suffice: New Bounds and Algorithms For Tolls in Single Source Networks. Theoretical Computer Science 348(2-3), 217–225 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  17. Goldberg, P.W.: Bounds for the Convergence Rate of Randomized Local Search in a Multiplayer Load-Balancing Game. In: PODC 2004: Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing, pp. 131–140. ACM, New York (2004)

    Chapter  Google Scholar 

  18. Harris, C.: On the Rate of Convergence of Continuous-Time Fictitious Play. Games and Economic Behavior 22(2), 238–259 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  19. Hirsch, M.W., Smale, S., Devaney, R.: Differential Equations, Dynamical Systems, and an Introduction to Chaos. Elsevier Academic Press, Amsterdam (2003)

    Google Scholar 

  20. Hofbauer, J., Sigmund, K.: Evolutionary Game Dynamics. Bulletin of the American Mathematical Society 4, 479–519 (2003)

    Article  MathSciNet  Google Scholar 

  21. Hofbauer, J., Sorin, S.: Best Response Dynamics for Continuous Zero-Sum Games. Discrete and Continuous Dynamical Systems-Series B 6(1) (2006)

    Google Scholar 

  22. Koutsoupias, E., Papadimitriou, C.: Worst-case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  23. Thathachar, M.A.L., Narendra, K.S.: Learning Automata: An Introduction. Prentice Hall, Englewood Cliffs (1989)

    Google Scholar 

  24. Kushner, H.J.: Approximation and Weak Convergence Methods for Random Processes, with Applications to Stochastic Systems Theory. MIT Press, Cambridge (1984)

    MATH  Google Scholar 

  25. Libman, L., Orda, A.: Atomic Resource Sharing in Noncooperative Networks. Telecommunication Systems 17(4), 385–409 (2001)

    Article  MATH  Google Scholar 

  26. Nash, J.F.: Equilibrium Points in n-person Games. Proc. of the National Academy of Sciences 36, 48–49 (1950)

    Article  MATH  MathSciNet  Google Scholar 

  27. Orda, A., Rom, R., Shimkin, N.: Competitive Routing in Multi-user Communication Networks. IEEE/ACM Transactions on Networking (TON) 1(5), 510–521 (1993)

    Article  Google Scholar 

  28. Thathachar, M.A.L., Sastry, P.S., Phansalkar, V.V.: Decentralized Learning of Nash Equilibria in Multi-Person Stochastic Games With Incomplete Information. IEEE transactions on system, man, and cybernetics 24(5) (1994)

    Google Scholar 

  29. Roughgarden, T.: How unfair is optimal routing? In: Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 203–204 (2002)

    Google Scholar 

  30. Roughgarden, T., Tardos, É.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)

    Article  MathSciNet  Google Scholar 

  31. Olbrich, L., Fischer, S., Vöcking, B.: Approximating Wardrop Equilibria with Finitely Many Agents. In: Pelc, A. (ed.) DISC 2007. LNCS, vol. 4731, pp. 238–252. Springer, Heidelberg (2007)

    Google Scholar 

  32. Stroock, D.W., Varadhan, S.R.S.: Multidimensional Diffusion Processes. Springer, Heidelberg (1979)

    MATH  Google Scholar 

  33. Vöcking, B.: Selfish Load Balancing. In: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)

    Google Scholar 

  34. Wardrop, J.: Some Theoretical Aspects of Road Traffic Research. Proceedings of the Institution of Civil Engineers, Part II 1(36), 352–362 (1952)

    Google Scholar 

  35. Weibull, J.W.: Evolutionary Game Theory. The MIT Press, Cambridge (1995)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. LORIA/INRIA-CNRS-UHP,  , 615 Rue du Jardin Botanique, 54602, Villers-Lès-Nancy, France

    Olivier Bournez, Octave Boussaton & Johanne Cohen

  2. Laboratoire PRiSM Université de Versailles, 45, avenue des Etats-Unis, 78000, Versailles, France

    Dominique Barth

Authors
  1. Dominique Barth
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Olivier Bournez
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Octave Boussaton
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Johanne Cohen
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Cristian S. Calude José Félix Costa Rudolf Freund Marion Oswald Grzegorz Rozenberg

Rights and permissions

Reprints and permissions

Copyright information

© 2008 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Barth, D., Bournez, O., Boussaton, O., Cohen, J. (2008). Distributed Learning of Wardrop Equilibria. In: Calude, C.S., Costa, J.F., Freund, R., Oswald, M., Rozenberg, G. (eds) Unconventional Computing. UC 2008. Lecture Notes in Computer Science, vol 5204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85194-3_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-540-85194-3_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85193-6

  • Online ISBN: 978-3-540-85194-3

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation