Abstract
Network routing games, and more generally congestion games play a central role in algorithmic game theory, comparable to the role of the traveling salesman problem in combinatorial optimization. It is known that the price of anarchy is independent of the network topology for non-atomic congestion games. In other words, it is independent of the structure of the strategy spaces of the players, and for affine cost functions it equals 4/3. In this paper, we show that the situation is considerably more intricate for atomic congestion games. More specifically, we consider congestion games with affine cost functions where the players’ strategy spaces are symmetric and equal to the set of bases of a k-uniform matroid. In this setting, we show that the price of anarchy is strictly larger than the price of anarchy for singleton strategy spaces where it is 4/3. As our main result we show that the price of anarchy can be bounded from above by \(28/13 \approx 2.15\). This constitutes a substantial improvement over the price of anarchy bound 5/2, which is known to be tight for network routing games with affine cost functions.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Abed, F., Correa, J.R., Huang, C.-C.: Optimal coordination mechanisms for multi-job scheduling games. In: Schulz, A.S., Wagner, D. (eds.) ESA 2014. LNCS, vol. 8737, pp. 13–24. Springer, Heidelberg (2014)
Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. J. ACM 55(6), 1–22 (2008)
Ackermann, H., Röglin, H., Vöcking, B.: Pure Nash equilibria in player-specific and weighted congestion games. Theoret. Comput. Sci. 410(17), 1552–1563 (2009)
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)
Awerbuch, B., Azar, Y., Epstein, A.: The price of routing unsplittable flow. In: Proceedings of the 37th Annual ACM Symposium Theory Computing, pp. 57–66 (2005)
Beckmann, M., McGuire, C.B., Winsten, C.B.: Studies in the Economics and Transportation. Yale University Press, New Haven (1956)
Braess, D.: Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung 12, 258–0268 (1968). (German)
Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4051, pp. 311–322. Springer, Heidelberg (2006)
Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proceedings of the 37th Annual ACM Symposium Theory Computing, pp. 67–73 (2005)
de Jong, J., Klimm, M., Uetz, M.: Efficiency of equilibria in uniform matroid congestion games. CTIT Technical report TR-CTIT-16-04, University of Twente (2016). http://eprints.eemcs.utwente.nl/26855/
Dunkel, J., Schulz, A.S.: On the complexity of pure-strategy Nash equilibria in congestion and local-effect games. Math. Oper. Res. 33(4), 851–868 (2008)
Fotakis, D.: Stackelberg strategies for atomic congestion games. Theory Comput. Syst. 47, 218–249 (2010)
Fujishige, S., Goemans, M.X., Harks, T., Peis, B., Zenklusen, R.: Matroids are immune to Braess paradox. arXiv:1504.07545 (2015)
Gairing, M., Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: Nash equilibria in discrete routing games with convex latency functions. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 645–657. Springer, Heidelberg (2004)
Gairing, M., Schoppmann, F.: Total latency in singleton congestion games. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 381–387. Springer, Heidelberg (2007)
Goemans, M.X., Mirrokni, V.S., Vetta, A.: Sink equilibria and convergence. In: Proceedings of the 46th Annual IEEE Symposium Foundations of Computer Science, pp. 142–154 (2005)
Harks, T., Klimm, M., Peis, B.: Resource competition on integral polymatroids. In: Liu, T.-Y., Qi, Q., Ye, Y. (eds.) WINE 2014. LNCS, vol. 8877, pp. 189–202. Springer, Heidelberg (2014)
Harks, T., Peis, B.: Resource buying games. Algorithmica 70(3), 493–512 (2014)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Lücking, T., Mavronicolas, M., Monien, B., Rode, M.: A new model for selfish routing. Theoret. Comput. Sci. 406(3), 187–206 (2008)
Meyers, C., Problems, N.F., Games, C.: Complexity and approximation results. Ph.D. thesis, MIT, Operations Research Center (2006)
Milchtaich, I.: Congestion games with player-specific payoff functions. Games Econom. Behav. 13(1), 111–124 (1996)
Pigou, A.C.: The Economics of Welfare. Macmillan, London (1920)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. Internat. J. Game Theory 2(1), 65–67 (1973)
Rosenthal, R.W.: The network equilibrium problem in integers. Networks 3, 53–59 (1973)
Roughgarden, T.: The price of anarchy is independent of the network topology. J. Comput. System Sci. 67, 341–364 (2002)
Roughgarden, T., Tardos, É.: How bad is selfish routing? J. ACM 49(2), 236–259 (2002)
Suri, S., Tóth, C.D., Zhou, Y.: Selfish load balancing and atomic congestion games. Algorithmica 47(1), 79–96 (2007)
Tran-Thanh, L., Polukarov, M., Chapman, A., Rogers, A., Jennings, N.R.: On the existence of pure strategy nash equilibria in integer–splittable weighted congestion games. In: Persiano, G. (ed.) SAGT 2011. LNCS, vol. 6982, pp. 236–253. Springer, Heidelberg (2011)
Wardrop, J.G.: Some theoretical aspects of road traffic research. Proc. Inst. Civ. Eng. 1(3), 325–362 (1952)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Jong, J., Klimm, M., Uetz, M. (2016). Efficiency of Equilibria in Uniform Matroid Congestion Games. In: Gairing, M., Savani, R. (eds) Algorithmic Game Theory. SAGT 2016. Lecture Notes in Computer Science(), vol 9928. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-53354-3_9
Download citation
DOI: https://doi.org/10.1007/978-3-662-53354-3_9
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-53353-6
Online ISBN: 978-3-662-53354-3
eBook Packages: Computer ScienceComputer Science (R0)