Advertisement

A Selective Tour Through Congestion Games

  • Dimitris FotakisEmail author
Chapter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9295)

Abstract

We give a sketchy and mostly informal overview of research on algorithmic properties of congestion games in the last ten years. We discuss existence of potential functions and pure Nash equilibria in games with weighted players, simple and fast algorithms that reach a pure Nash equilibrium, and efficient approaches to improving the Price of Anarchy.

Keywords

Nash Equilibrium Delay Function Congestion Game Optimal Toll Pure Nash Equilibrium 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structre on congestion games. J. Assoc. Comput. Mach. 55(6), 1–22 (2008)CrossRefzbMATHGoogle Scholar
  2. 2.
    Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. SIAM J. Comput. 40(5), 1211–1233 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    Althöfer, I.: On sparse approximations to randomized strategies and convex combinations. Linear Algebra Appl. 99, 339–355 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Ashlagi, I., Krysta, P., Tennenholtz, M.: Social context games. In: Papadimitriou, C., Zhang, S. (eds.) WINE 2008. LNCS, vol. 5385, pp. 675–683. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  6. 6.
    Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC 2005), pp. 57–66 (2005)Google Scholar
  7. 7.
    Barman, S.: Approximating Carathéodory’s theorem and nash equilibria. In: Proceedings of the 47th ACM Symposium on Theory of Computing (STOC 2015) (2015)Google Scholar
  8. 8.
    Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)Google Scholar
  9. 9.
    Bonifaci, V., Harks, T., Schäfer, G.: Stackelberg routing in arbitrary networks. Math. Oper. Res. 35(2), 330–346 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Braess, D.: Über ein paradox aus der Verkehrsplanung. Unternehmensforschung 12, 258–268 (1968)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. Algorithmica 61(3), 606–637 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Caragiannis, I., Kaklamanis, C., Kanellopoulos, P.: Taxes for linear atomic congestion games. ACM Trans. Algorithms 7(1), 13 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Christodoulou, G., Koutsoupias, E.: The Price of anarchy of finite congestion games. In: Proceedings of the 37th ACM Symposium on Theory of Computing (STOC 2005), pp. 67–73 (2005)Google Scholar
  14. 14.
    Christodoulou, G., Koutsoupias, E., Spirakis, P.G.: On the performance of approximate equilibria in congestion games. Algorithmica 61(1), 116–140 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Chung, F., Young, S.J.: Braess’s paradox in large sparse graphs. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 194–208. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  16. 16.
    Cole, R., Dodis, Y., Roughgarden, T.: How much can taxes help selfish routing? J. Comput. Syst. Sci. 72(3), 444–467 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Correa, J.R., Schulz, A.S., Stier, N.E.: Moses. selfish routing in capacitated networks. Math. Oper. Res. 29(4), 961–976 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Correa, J.R., Stier-Moses, N.E.: Stackelberg Routing in Atomic Network Games. In: Technical report DRO-2007-03, Columbia Business School (2007)Google Scholar
  19. 19.
    Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure nash equilibria. In: Proceedings of the 36th ACM Symposium on Theory of Computing (STOC 2004), pp. 604–612 (2004)Google Scholar
  20. 20.
    Fleischer, L., Jain, K., Mahdian, M.: Tolls for heterogeneous selfish users in multicommodity networks and generalized congestion games. In: Proceedings of the 45th IEEE Symposium on Foundations of Computer Science (FOCS 2004), pp. 277–285 (2004)Google Scholar
  21. 21.
    Fotakis, D.: Stackelberg strategies for atomic congestion games. Theory Comput. Syst. 47(1), 218–249 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Fotakis, D.: Congestion games with linearly independent paths: convergence time and price of anarchy. Theory Comput. Syst. 47(1), 113–136 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Fotakis, D., Gkatzelis, V., Kaporis, A.C., Spirakis, P.G.: The impact of social ignorance on weighted congestion games. Theory Comput. Syst. 50(3), 559–578 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Fotakis, D., Kaporis, A.C., Spirakis, P.G.: Efficient methods for selfish network design. Theor. Comput. Sci. 448, 9–20 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Fotakis, D., Kaporis, A.C., Lianeas, T., Spirakis, P.G.: Resolving braess’s paradox in random networks. In: Chen, Y., Immorlica, N. (eds.) WINE 2013. LNCS, vol. 8289, pp. 188–201. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  26. 26.
    Fotakis, D., Kaporis, A.C., Spirakis, P.G.: Atomic congestion games: fast, myopic and concurrent. Theory Comput. Syst. 47(1), 38–59 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  27. 27.
    Fotakis, D., Kaporis, A.C., Spirakis, P.G.: Efficient methods for selfish network design. Theor. Comput. Sci. 448, 9–20 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  28. 28.
    Fotakis, D., Karakostas, G., Kolliopoulos, S.G.: On the existence of optimal taxes for network congestion games with heterogeneous users. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 162–173. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  29. 29.
    Fotakis, D., Kontogiannis, S.C., Koutsoupias, E., Mavronicolas, M., Spirakis, P.G.: The structure and complexity of Nash equilibria for a selfish routing game. Theor. Comput. Sci. 410(36), 3305–3326 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  30. 30.
    Fotakis, D., Kontogiannis, S.C., Spirakis, P.G.: Selfish unsplittable flows. Theor. Comput. Sci. 348, 226–239 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  31. 31.
    Fotakis, D.A., Kontogiannis, S.C., Spirakis, P.G.: 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) CrossRefGoogle Scholar
  32. 32.
    Fotakis, D., Spirakis, P.G.: Cost-balancing tolls for atomic network congestion games. Internet Math. 5(4), 343–363 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  33. 33.
    Gairing, M., Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: Nash equilibria in discrete routing games with convex latency functions. J. Comput. Syst. Sci. 74(7), 1199–1225 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Harks, T., Klimm, M., Möhring, R.H.: Characterizing the existence of potential functions in weighted congestion games. Theory Comput. Syst. 49(1), 46–70 (2011)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Holzman, R., Law-Yone, N.: (Lev-tov). Network structure and strong equilibrium in route selection games. Math. Soc. Sci. 46, 193–205 (2003)CrossRefzbMATHGoogle Scholar
  36. 36.
    Kaporis, A.C., Spirakis, P.G.: The price of optimum in Stackelberg games on arbitrary single commodity networks and latency functions. Theor. Comput. Sci. 410(8–10), 745–755 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  37. 37.
    Karakostas, G., Kolliopoulos, S.: Edge pricing of multicommodity networks for heterogeneous selfish users. In: Proceedings of the 45th IEEE Symposium on Foundations of Computer Science (FOCS 2004), pp. 268–276 (2004)Google Scholar
  38. 38.
    Karakostas, G., Kolliopoulos, S.: Stackelberg strategies for selfish routing in general multicommodity networks. Algorithmica 53(1), 132–153 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  39. 39.
    Korilis, Y.A., Lazar, A.A., Orda, A.: Achieving network optima using Stackelberg routing strategies. IEEE/ACM Trans. Networking 5(1), 161–173 (1997)CrossRefGoogle Scholar
  40. 40.
    Koutsoupias, E., Mavronicolas, M., Spirakis, P.: Approximate equilibria and ball fusion. Theory Comput. Syst. 36, 683–693 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. Comput. Sci. Rev. 3(2), 65–69 (2009)CrossRefzbMATHGoogle Scholar
  42. 42.
    Lipton, R.J., Markakis, E., Mehta, A.: Playing large games using simple strategies. In: Proceedings of the 4th ACM Conference on Electronic Commerce (EC 2003), pp. 36–41 (2003)Google Scholar
  43. 43.
    Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: A new model for selfish routing. Theor. Comput. Sci. 406(3), 187–206 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  44. 44.
    Mavronicolas, M., Spirakis, P.G.: The price of selfish routing. Algorithmica 48(1), 91–126 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  45. 45.
    Milchtaich, I.: Network topology and the efficiency of equilibrium. Games Econ. Behav. 57, 321–346 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  46. 46.
    Monderer, D., Shapley, L.: Potential games. Games Econ. Behav. 14, 124–143 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  47. 47.
    Panagopoulou, P.N., Spirakis, P.G.: Algorithms for pure Nash equilibria in weighted congestion games. ACM J. Exp. Algorithmics 11, 1–19 (2006)MathSciNetzbMATHGoogle Scholar
  48. 48.
    Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibria. Int. J. Game Theory 2, 65–67 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  49. 49.
    Roughgarden, T.: The price of anarchy is independent of the network topology. In: Proceedings of the 34th ACM Symposium on Theory of Computing (STOC 2002), pp. 428–437 (2002)Google Scholar
  50. 50.
    Roughgarden, T.: Stackelberg scheduling strategies. SIAM J. Comput. 33(2), 332–350 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  51. 51.
    Roughgarden, T.: On the severity of Braess’s paradox: designing networks for selfish users is hard. J. Comput. Syst. Sci. 72(5), 922–953 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  52. 52.
    Swamy, C.: The effectiveness of stackelberg strategies and tolls for network congestion games. In: Proceedings of the 18th ACM-SIAM Symposium on Discrete Algorithms (SODA 2007), pp. 1133–1142 (2007)Google Scholar
  53. 53.
    Valiant, G., Roughgarden, T.: Braess’s paradox in large random graphs. Random Struct. Algorithms 37(4), 495–515 (2010)MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Division of Computer Science, School of Electrical and Computer EngineeringNational Technical University of AthensAthensGreece

Personalised recommendations