Edge Pricing of Multicommodity Networks for Selfish Users with Elastic Demands

  • George Karakostas
  • Stavros G. Kolliopoulos
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4112)


We examine how to induce selfish heterogeneous users in a multicommodity network to reach an equilibrium that minimizes the social cost. In the absence of centralized coordination, we use the classical method of imposing appropriate taxes (tolls) on the edges of the network. We significantly generalize previous work [20,13,9] by allowing user demands to be elastic. In this setting the demand of a user is not fixed a priori but it is a function of the routing cost experienced, a most natural assumption in traffic and data networks.


Complementarity Problem Elastic Demand Optimal Taxis Congestion Game User Class 
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  1. 1.
    Aashtiani, H.Z., Magnanti, T.L.: Equilibria on a congested transportation network. SIAM J. Algebraic and Discrete Methods 2, 213–226 (1981)MATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press (1956)Google Scholar
  3. 3.
    Cole, R., Dodis, Y., Roughgarden, T.: Pricing network edges for heterogeneous selfish users. In: Proc. 35th ACM STOC, pp. 521–530 (2003)Google Scholar
  4. 4.
    Cole, R., Dodis, Y., Roughgarden, T.: Bottleneck links, variable demand and the tragedy of the commons. In: Proc. 17th ACM-SIAM SODA, pp. 668–677 (2006)Google Scholar
  5. 5.
    Dafermos, S.C.: Traffic equilibria and variational inequalities. Transportation Science 14, 42–54 (1980)CrossRefMathSciNetGoogle Scholar
  6. 6.
    Dafermos, S., Sparrow, F.T.: The traffic assignment problem for a general network. J. Research National Bureau of Standards, Series B 73B, 91–118 (1969)MathSciNetGoogle Scholar
  7. 7.
    Dafermos, S.: Toll patterns for multiclass-user transportation networks. Transportation Science 7, 211–223 (1973)CrossRefGoogle Scholar
  8. 8.
    Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. 1. Springer, Berlin (2003)Google Scholar
  9. 9.
    Fleischer, L., Jain, K., Mahdian, M.: Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games. In: Proc. 45th IEEE Symposium on Foundations of Computer Science, pp. 277–285 (2004)Google Scholar
  10. 10.
    Gartner, N.H.: Optimal traffic assignment with elastic demands: a review. Part I: analysis framework. Transportation Science 14, 174–191 (1980)CrossRefMathSciNetGoogle Scholar
  11. 11.
    Gartner, N.H.: Optimal traffic assignment with elastic demands: a review. Part II: algorithmic approaches. Transportation Science 14, 192–208 (1980)CrossRefMathSciNetGoogle Scholar
  12. 12.
    Hearn, D.W., Yildirim, M.B.: A toll pricing framework for traffic assignment problems with elastic demand. In: Gendreau, M., Marcotte, P. (eds.) Transportation and Network Analysis: Current Trends. Miscellanea in honor of Michael Florian. Kluwer Academic Publishers, Dordrecht (2002)Google Scholar
  13. 13.
    Karakostas, G., Kolliopoulos, S.G.: Edge pricing of multicommodity networks for heterogeneous selfish users. In: Proc. 45th IEEE Symposium on Foundations of Computer Science, pp. 268–276 (2004)Google Scholar
  14. 14.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Proc. 16th Symposium on Theoretical Aspects of Computer Science, pp. 404–413 (1999)Google Scholar
  15. 15.
    Nagurney, A.: A multiclass, multicriteria traffic network equilibrium model. Mathematical and Computer Modelling 32, 393–411 (2000)MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)MATHGoogle Scholar
  17. 17.
    Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49, 236–259 (2002)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Todd, M.J.: The computation of fixed points and applications. Lecture Notes in Economics and Mathematical Systems, vol. 124. Springer, Heidelberg (1976)MATHGoogle Scholar
  19. 19.
    Wardrop, J.G.: Some theoretical aspects of road traffic research. Proc. Inst. Civil Engineers, Part II 1, 325–378 (1952)Google Scholar
  20. 20.
    Yang, H., Huang, H.-J.: The multi-class, multi-criteria traffic network equilibrium and systems optimum problem. Transportation Research Part B 38, 1–15 (2004)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • George Karakostas
    • 1
  • Stavros G. Kolliopoulos
    • 2
  1. 1.Department of Computing and SoftwareMcMaster University 
  2. 2.Department of Informatics and TelecommunicationsUniversity of Athens 

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