The Impact of Social Ignorance on Weighted Congestion Games
We consider weighted linear congestion games, and investigate how social ignorance, namely lack of information about the presence of some players, affects the inefficiency of pure Nash equilibria (PNE) and the convergence rate of the ε-Nash dynamics. To this end, we adopt the model of graphical linear congestion games with weighted players, where the individual cost and the strategy selection of each player only depends on his neighboring players in the social graph. We show that such games admit a potential function, and thus a PNE. Our main result is that the impact of social ignorance on the Price of Anarchy (PoA) and the Price of Stability (PoS) is naturally quantified by the independence numberα(G) of the social graph G. In particular, we show that the PoA grows roughly as α(G)(α(G) + 2), which is essentially tight as long as α(G) does not exceed half the number of players, and that the PoS lies between α(G) and 2α(G). Moreover, we show that the ε-Nash dynamics reaches an α(G)(α(G) + 2)-approximate configuration in polynomial time that does not directly depend on the social graph. For unweighted graphical linear games with symmetric strategies, we show that the ε-Nash dynamics reaches an ε-approximate PNE in polynomial time that exceeds the corresponding time for symmetric linear games by a factor at most as large as the number of players.
Unable to display preview. Download preview PDF.
- 1.Ackermann, H., Röglin, H., Vöcking, B.: On the Impact of Combinatorial Structure on Congestion Games. Journal of the ACM 55(6) (2008)Google Scholar
- 3.Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, É., Wexler, T., Roughgarden, T.: The Price of Stability for Network Design with Fair Cost Allocation. In: Proc. of the 45th IEEE Symp. on Foundations of Computer Science (FOCS 2004), pp. 295–304 (2004)Google Scholar
- 5.Awerbuch, B., Azar, Y., Epstein, A.: The Price of Routing Unsplittable Flow. In: Proc. of the 37th ACM Symp. on Theory of Computing (STOC 2005), pp. 57–66 (2005)Google Scholar
- 6.Awerbuch, B., Azar, Y., Epstein, A., Mirrokni, V., Skopalik, A.: Fast Convergence to Nearly Optimal Solutions in Potential Games. In: Proc. of the 9th ACM Conf. on Electronic Commerce (EC 2008), pp. 264–273 (2008)Google Scholar
- 10.Chien, S., Sinclair, A.: Convergece to Approximate Nash Equilibria in Congestion Games. In: Proc. of the 18th Symp. on Discrete Algorithms (SODA 2007), pp. 169–178 (2007)Google Scholar
- 12.Christodoulou, G., Koutsoupias, E.: The Price of Anarchy of Finite Congestion Games. In: Proc. of the 37th ACM Symp. on Theory of Computing (STOC 2005), pp. 67–73 (2005)Google Scholar
- 13.Christodoulou, G., Koutsoupias, E., Spirakis, P.: On the Performance of Approximate Equilibria in Congestion Games. In: Proc. of the 17th European Symposium on Algorithms (ESA 2009). LNCS, vol. 5757. Springer, Heidelberg (2009)Google Scholar
- 14.Fabrikant, A., Papadimitriou, C., Talwar, K.: The Complexity of Pure Nash Equilibria. In: Proc. of the 36th ACM Symp. on Theory of Computing (STOC 2004), pp. 604–612 (2004)Google Scholar
- 21.Skopalik, A., Vöcking, B.: Inapproximability of Pure Nash Equilibria. In: Proc. of the 40th ACM Symp. on Theory of Computing (STOC 2008), pp. 355–364 (2008)Google Scholar