Abstract
The Price of Anarchy in congestion games has attracted a lot of research over the last decade. This resulted in a thorough understanding of this concept. In contrast the Price of Stability, which is an equally interesting concept, is much less understood.
In this paper, we consider congestion games with polynomial cost functions with nonnegative coefficients and maximum degree d. We give matching bounds for the Price of Stability in such games, i.e., our technique provides the exact value for any degree d.
For linear congestion games, tight bounds were previously known. Those bounds hold even for the more restricted case of dominant equilibria, which may not exist. We give a separation result showing that already for congestion games with quadratic cost functions this is not possible; that is, the Price of Anarchy for the subclass of games that admit a dominant strategy equilibrium is strictly smaller than the Price of Stability for the general class.
This work was supported by EPSRC grants EP/K01000X/1 and EP/J019399/1.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Aland, S., Dumrauf, D., Gairing, M., Monien, B., Schoppmann, F.: Exact price of anarchy for polynomial congestion games. SIAM Journal on Computing 40(5), 1211–1233 (2011)
Albers, S.: On the value of coordination in network design. SIAM Journal on Computing 38(6), 2273–2302 (2009)
Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM Journal on Computing 38(4), 1602–1623 (2008)
Awerbuch, B., Azar, Y., Epstein, A.: Large the price of routing unsplittable flow. In: Proceedings of STOC, pp. 57–66 (2005)
Bhawalkar, K., Gairing, M., Roughgarden, T.: Weighted congestion games: Price of anarchy, universal worst-case examples, and tightness. In: de Berg, M., Meyer, U. (eds.) ESA 2010, Part II. LNCS, vol. 6347, pp. 17–28. Springer, Heidelberg (2010)
Bilò, V.: A unifying tool for bounding the quality of non-cooperative solutions in weighted congestion games. In: Erlebach, T., Persiano, G. (eds.) WAOA 2012. LNCS, vol. 7846, pp. 215–228. Springer, Heidelberg (2013)
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)
Bilò, V., Caragiannis, I., Fanelli, A., Monaco, G.: Improved lower bounds on the price of stability of undirected network design games. In: Kontogiannis, S., Koutsoupias, E., Spirakis, P.G. (eds.) SAGT 2010. LNCS, vol. 6386, pp. 90–101. Springer, Heidelberg (2010)
Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. Algorithmica 61, 606–637 (2011)
Chen, H.-L., Roughgarden, T.: Network design with weighted players. Theory of Computing Systems 45, 302–324 (2009)
Christodoulou, G., Koutsoupias, E.: The price of anarchy of finite congestion games. In: Proceedings of STOC, pp. 67–73 (2005)
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)
Christodoulou, G., Koutsoupias, E.: On the price of anarchy and stability of correlated equilibria of linear congestion games. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 59–70. Springer, Heidelberg (2005)
Christodoulou, G., Koutsoupias, E., Spirakis, P.G.: On the performance of approximate equilibria in congestion games. Algorithmica 61(1), 116–140 (2011)
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. CoRR, abs/1211.2090 (2012); To appear in CIAC 2013
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)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Li, J.: An \(O(\frac{\log n}{\log\log n})\) upper bound on the price of stability for undirected Shapley network design games. Information Processing Letters 109(15), 876–878 (2009)
Monderer, D., Shapley, L.: Potential games. Games and Economics Behavior 14, 124–143 (1996)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)
Roughgarden, T.: Intrinsic robustness of the price of anarchy. Communications of the ACM 55(7), 116–123 (2012)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Christodoulou, G., Gairing, M. (2013). Price of Stability in Polynomial Congestion Games. In: Fomin, F.V., Freivalds, R., Kwiatkowska, M., Peleg, D. (eds) Automata, Languages, and Programming. ICALP 2013. Lecture Notes in Computer Science, vol 7966. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39212-2_44
Download citation
DOI: https://doi.org/10.1007/978-3-642-39212-2_44
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-39211-5
Online ISBN: 978-3-642-39212-2
eBook Packages: Computer ScienceComputer Science (R0)