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Capacitated Network Design Games

  • Michal Feldman
  • Tom Ron
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7615)

Abstract

We study a capacitated symmetric network design game, where each of n agents wishes to construct a path from a network’s source to its sink, and the cost of each edge is shared equally among its agents. The uncapacitated version of this problem has been introduced by Anshelevich et al. (2003) and has been extensively studied. We find that the consideration of edge capacities entails a significant effect on the quality of the obtained Nash equilibria (NE), under both the utilitarian and the egalitarian objective functions, as well as on the convergence rate to an equilibrium. The following results are established. First, we provide bounds for the price of anarchy (PoA) and the price of stability (PoS) measures with respect to the utilitarian (i.e., sum of costs) and egalitarian (i.e., maximum cost) objective functions. Our main result here is that, unlike the uncapacitated version, the network topology is a crucial factor in the quality of NE. Specifically, a network topology has a bounded PoA if and only if it is series-parallel (SP). Second, we show that the convergence rate of best-response dynamics (BRD) may be super linear (in the number of agents). This is in contrast to the uncapacitated version, where convergence is guaranteed within at most n iterations.

Keywords

Nash Equilibrium Network Topology Congestion Game Potential Game Strong 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.

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References

  1. 1.
    Albers, S.: On the value of coordination in network design. In: Proceedings of the Nineteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2008, pp. 294–303. Society for Industrial and Applied Mathematics, Philadelphia (2008)Google Scholar
  2. 2.
    Andelman, N., Feldman, M., Mansour, Y.: Strong Price of Anarchy. In: SODA 2007 (2007)Google Scholar
  3. 3.
    Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science, pp. 295–304. IEEE Computer Society, Washington, DC (2004)CrossRefGoogle Scholar
  4. 4.
    Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-optimal network design with selfish agents. In: STOC, pp. 511–520 (2003)Google Scholar
  5. 5.
    Bala, V., Goyal, S.: A noncooperative model of network formation. Econometrica 68(5), 1181–1230 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Corbo, J., Parkes, D.: The price of selfish behavior in bilateral network formation. In: Proceedings of the Twenty-Fourth Annual ACM Symposium on Principles of Distributed Computing, PODC 2005, pp. 99–107. ACM, New York (2005)Google Scholar
  7. 7.
    Devanur, N.R., Mihail, M., Vazirani, V.V.: Strategyproof cost-sharing mechanisms for set cover and facility location games. In: Proc. of ACM EC, pp. 108–114 (2003)Google Scholar
  8. 8.
    Epstein, A., Feldman, M., Mansour, Y.: Strong equilibrium in cost sharing connection games. In: Proceedings of the 8th ACM Conference on Electronic Commerce, EC 2007, pp. 84–92. ACM, New York (2007)Google Scholar
  9. 9.
    Epstein, A., Feldman, M., Mansour, Y.: Efficient graph topologies in network routing games. Games and Economic Behavior 66(1), 115–125 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence Time to Nash Equilibria. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 502–513. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  11. 11.
    Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure nash equilibria. In: Proceedings of the Thirty-Sixth Annual ACM Symposium on Theory of Computing, STOC 2004, pp. 604–612. ACM, New York (2004)CrossRefGoogle Scholar
  12. 12.
    Feldman, M., Tamir, T.: Convergence rate of best response dynamics in scheduling games with conflicting congestion effects. Working paper (2011)Google Scholar
  13. 13.
    Fotakis, D.: Congestion games with linearly independent paths: Convergence time and price of anarchy. Theory Comput. Syst. 47(1), 113–136 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Garey, M.R., Johnson, D.S.: Computers and Intractability; A Guide to the Theory of NP-Completeness. W. H. Freeman & Co., New York (1990)Google Scholar
  15. 15.
    Holzman, R., Law-Yone, N.: Strong equilibrium in congestion games. Games and Economic Behavior 21(1-2), 85–101 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Holzman, R., Law-Yone (Lev-tov), N.: Network structure and strong equilibrium in route selection games. Mathematical Social Sciences 46(2), 193–205 (2003)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Koutsoupias, E., Papadimitriou, C.: Worst-Case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)CrossRefGoogle Scholar
  18. 18.
    Chen, H.L., Roughgarden, T.: Network design with weighted players. In: Proceedings of the 18th ACM Symposium on Parallelism in Algorithms and Architextures (SPAA), pp. 29–38 (2006)Google Scholar
  19. 19.
    Milchtaich, I.: Topological conditions for uniqueness of equilibrium in networks. Mathematics of Operations Research 30, 225–244 (2005)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Milchtaich, I.: The Equilibrium Existence Problem in Finite Network Congestion Games. In: Spirakis, P.G., Mavronicolas, M., Kontogiannis, S.C. (eds.) WINE 2006. LNCS, vol. 4286, pp. 87–98. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  21. 21.
    Milchtaich, I.: Network topology and the efficiency of equilibrium. Games and Economic Behavior 57(2), 321–346 (2006)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Monderer, D.: Potential games. Games and Economic Behavior 14(1), 124–143 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Papadimitriou, C.: Algorithms, games, and the internet. In: Proceedings of the Thirty-Third Annual ACM Symposium on Theory of Computing, STOC 2001, pp. 749–753. ACM, New York (2001)CrossRefGoogle Scholar
  24. 24.
    Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibria. International Journal of Game Theory 2(1), 65–67 (1973)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Michal Feldman
    • 1
    • 2
  • Tom Ron
    • 1
  1. 1.Hebrew University of JerusalemIsrael
  2. 2.Harvard UniversityUSA

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