Capacitated Network Design Games
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.
KeywordsNash Equilibrium Network Topology Congestion Game Potential Game Strong Equilibrium
Unable to display preview. Download preview PDF.
- 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.Andelman, N., Feldman, M., Mansour, Y.: Strong Price of Anarchy. In: SODA 2007 (2007)Google Scholar
- 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.Anshelevich, E., Dasgupta, A., Tardos, É., Wexler, T.: Near-optimal network design with selfish agents. In: STOC, pp. 511–520 (2003)Google Scholar
- 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.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.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
- 12.Feldman, M., Tamir, T.: Convergence rate of best response dynamics in scheduling games with conflicting congestion effects. Working paper (2011)Google Scholar
- 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
- 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