MFCS 2014: Mathematical Foundations of Computer Science 2014 pp 541-552 | Cite as
An Hn/2 Upper Bound on the Price of Stability of Undirected Network Design Games
Abstract
In the network design game with n players, every player chooses a path in an edge-weighted graph to connect her pair of terminals, sharing costs of the edges on her path with all other players fairly. We study the price of stability of the game, i.e., the ratio of the social costs of a best Nash equilibrium (with respect to the social cost) and of an optimal play. It has been shown that the price of stability of any network design game is at most H n , the n-th harmonic number. This bound is tight for directed graphs. For undirected graphs, the situation is dramatically different, and tight bounds are not known. It has only recently been shown that the price of stability is at most \(H_n \left(1-\frac{1}{\Theta(n^4)} \right)\), while the worst-case known example has price of stability around 2.25. In this paper we improve the upper bound considerably by showing that the price of stability is at most H n/2 + ε for any ε starting from some suitable n ≥ n(ε).
Keywords
Nash Equilibrium Social Cost Social Optimum Tight Bound Harmonic NumberPreview
Unable to display preview. Download preview PDF.
References
- 1.Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: FOCS, pp. 295–304 (2004)Google Scholar
- 2.Asadpour, A., Saberi, A.: On the inefficiency ratio of stable equilibria in congestion games. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 545–552. Springer, Heidelberg (2009)CrossRefGoogle Scholar
- 3.Bilò, V., Bove, R.: Bounds on the price of stability of undirected network design games with three players. Journal of Interconnection Networks 12(1-2), 1–17 (2011)CrossRefGoogle Scholar
- 4.Bilò, V., Caragiannis, I., Fanelli, A., Monaco, G.: Improved lower bounds on the price of stability of undirected network design games. Theory Comput. Syst. 52(4), 668–686 (2013)CrossRefMATHMathSciNetGoogle Scholar
- 5.Bilò, V., Flammini, M., Moscardelli, L.: The price of stability for undirected broadcast network design with fair cost allocation is constant. In: FOCS, pp. 638–647 (2013)Google Scholar
- 6.Christodoulou, G., Chung, C., Ligett, K., Pyrga, E., van Stee, R.: On the price of stability for undirected network design. In: Bampis, E., Jansen, K. (eds.) WAOA 2009. LNCS, vol. 5893, pp. 86–97. Springer, Heidelberg (2010)CrossRefGoogle Scholar
- 7.Disser, Y., Feldmann, A.E., Klimm, M., Mihalák, M.: Improving the H k-bound on the price of stability in undirected shapley network design games. In: Spirakis, P.G., Serna, M. (eds.) CIAC 2013. LNCS, vol. 7878, pp. 158–169. Springer, Heidelberg (2013)CrossRefGoogle Scholar
- 8.Fanelli, A., Leniowski, D., Monaco, G., Sankowski, P.: The ring design game with fair cost allocation. In: Goldberg, P.W. (ed.) WINE 2012. LNCS, vol. 7695, pp. 546–552. Springer, Heidelberg (2012)CrossRefGoogle Scholar
- 9.Fiat, A., Kaplan, H., Levy, M., Olonetsky, S., Shabo, R.: On the price of stability for designing undirected networks with fair cost allocations. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 608–618. Springer, Heidelberg (2006)CrossRefGoogle Scholar
- 10.Li, J.: An upper bound on the price of stability for undirected shapley network design games. Information Processing Letters 109, 876–878 (2009)CrossRefMATHMathSciNetGoogle Scholar
- 11.Kawase, Y., Makino, K.: Nash equilibria with minimum potential in undirected broadcast games. Theor. Comput. Sci. 482, 33–47 (2013)CrossRefMATHMathSciNetGoogle Scholar
- 12.Lee, E., Ligett, K.: Improved bounds on the price of stability in network cost sharing games. In: EC, pp. 607–620 (2013)Google Scholar
- 13.Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14(1), 124–143 (1996)CrossRefMATHMathSciNetGoogle Scholar