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Exact Price of Anarchy for Polynomial Congestion Games

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STACS 2006 (STACS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3884))

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Abstract

We show exact values for the price of anarchy of weighted and unweighted congestion games with polynomial latency functions. The given values also hold for weighted and unweighted network congestion games.

This work has been partially supported by the DFG-SFB 376 and by the European Union within the 6th Framework Programme under contract 001907 (DELIS).

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References

  1. Awerbuch, B., Azar, Y., Epstein, A.: The Price of Routing Unsplittable Flow. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC 2005), pp. 57–66 (2005)

    Google Scholar 

  2. Awerbuch, B., Azar, Y., Richter, Y., Tsur, D.: Tradeoffs in Worst-Case Equilibria. In: Solis-Oba, R., Jansen, K. (eds.) WAOA 2003. LNCS, vol. 2909, pp. 41–52. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  3. Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press (1956)

    Google Scholar 

  4. Christodoulou, G., Koutsoupias, E.: On The Price of Anarchy and Stability of Correlated Equilibria of Linear Congestion Games. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 59–70. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  5. Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proc. of the 37th Annual ACM Symposium on Theory of Computing (STOC 2005), pp. 67–73 (2005)

    Google Scholar 

  6. Czumaj, A., Krysta, P., Vöcking, B.: Selfish Traffic Allocation for Server Farms. In: Proc. of the 34th Annual ACM Symposium on Theory of Computing (STOC 2002), pp. 287–296 (2002)

    Google Scholar 

  7. Czumaj, A., Vöcking, B.: Tight Bounds for Worst-Case Equilibria. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 413–420 (2002); Also accepted to Journal of Algorithms as Special Issue of SODA 2002

    Google Scholar 

  8. Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish Unsplittable Flows. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 593–605. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  9. Fotakis, D., Kontogiannis, S., Spirakis, P.: Symmetry in Network Congestion Games: Pure Equilibria and Anarchy Cost. In: Erlebach, T., Persinao, G. (eds.) WAOA 2005. LNCS, vol. 3879, pp. 161–175. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  10. Gairing, M., Lücking, T., Mavronicolas, M., Monien, B.: Computing Nash Equilibria for Scheduling on Restricted Parallel Links. In: Proc. of the 36th Annual ACM Symposium on Theory of Computing (STOC 2004), pp. 613–622 (2004)

    Google Scholar 

  11. Gairing, M., Lücking, T., Mavronicolas, M., Monien, B.: The Price of Anarchy for Polynomial Social Cost. In: Fiala, J., Koubek, V., Kratochvíl, J. (eds.) MFCS 2004. LNCS, vol. 3153, pp. 574–585. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  12. Gairing, M., Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: Nash Equilibria in Discrete Routing Games with Convex Latency Functions. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 645–657. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  13. Gairing, M., Lücking, T., Monien, B., Tiemann, K.: Nash Equilibria, the Price of Anarchy and the Fully Mixed Nash Equilibrium Conjecture. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 51–65. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  14. Gairing, M., Monien, B., Tiemann, K.: Selfish Routing with Incomplete Information. In: Proc. of the 17th Annual ACM Symposium on Parallel Algorithms and Architectures (SPAA 2005), pp. 203–212 (2005)

    Google Scholar 

  15. Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate Equilibria and Ball Fusion. Theory of Computing Systems 36(6), 683–693 (2003)

    Article  MathSciNet  MATH  Google Scholar 

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

    Chapter  Google Scholar 

  17. Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: A New Model for Selfish Routing. In: Diekert, V., Habib, M. (eds.) STACS 2004. LNCS, vol. 2996, pp. 547–558. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  18. Mas-Colell, A., Whinston, M.D., Green, J.R.: Microeconomic Theory. Oxford University Press, Oxford (1995)

    MATH  Google Scholar 

  19. McKelvey, R.D., McLennan, A.: Computation of Equilibria in Finite Games. Handbook of Computational Economics (1996)

    Google Scholar 

  20. Milchtaich, I.: Congestion Games with Player-Specific Payoff Functions. Games and Economic Behavior 13(1), 111–124 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  21. Monderer, D., Shapley, L.S.: Potential Games. Games and Economic Behavior 14(1), 124–143 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  22. Nash, J.F.: Equilibrium Points in n-Person Games. Proc. of the National Academy of Sciences of the United States of America 36, 48–49 (1950)

    Article  MathSciNet  MATH  Google Scholar 

  23. Nash, J.F.: Non-Cooperative Games. Annals of Mathematics 54(2), 286–295 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  24. Papadimitriou, C.H.: Algorithms, Games, and the Internet. In: Proc. of the 33rd Annual ACM Symposium on Theory of Computing (STOC 2001), pp. 749–753 (2001)

    Google Scholar 

  25. Rosenthal, R.W.: A Class of Games Possessing Pure-Strategy Nash Equilibria. Int. Journal of Game Theory 2, 65–67 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  26. Roughgarden, T.: How Unfair is Optimal Routing. In: Proc. of the 13th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA 2002), pp. 203–204 (2002)

    Google Scholar 

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

    MATH  Google Scholar 

  28. Roughgarden, T., Tardos, É.: How Bad Is Selfish Routing? Journal of the ACM 49(2), 236–259 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  29. Wardrop, J.G.: Some Theoretical Aspects of Road Traffic Research. In: Proc. of the Institute of Civil Engineers, Pt. II, vol. 1, pp. 325–378 (1952)

    Google Scholar 

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Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F. (2006). Exact Price of Anarchy for Polynomial Congestion Games. In: Durand, B., Thomas, W. (eds) STACS 2006. STACS 2006. Lecture Notes in Computer Science, vol 3884. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11672142_17

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  • DOI: https://doi.org/10.1007/11672142_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-32301-3

  • Online ISBN: 978-3-540-32288-7

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