Abstract
We present a short geometric proof for the price of anarchy results that have recently been established in a series of papers on selfish routing in multicommodity flow networks. This novel proof also facilitates two new types of results: On the one hand, we give pseudo-approximation results that depend on the class of allowable cost functions. On the other hand, we derive improved bounds on the inefficiency of Nash equilibria for situations in which the equilibrium travel times are within reasonable limits of the free-flow travel times. These tighter bounds help to explain empirical observations in vehicular traffic networks. Our analysis holds in the more general context of congestion games, which provides the framework in which we describe this work.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Beckmann, M.J., Mcguire, C.B., Winsten, C.B.: Studies in the Economics of Transportation. Yale University Press, New Haven (1956)
Bureau of Public Roads: Traffic assignment manual. U.S. Department of Commerce, Urban Planning Division, Washington, DC (1964)
Catoni, S., Pallotino, S.: Traffic equilibrium paradoxes. Transportation Science 25, 240–244 (1991)
Chakrabarty, D.: Improved bicriteria results for the selfish routing problem (2004) (Manuscript)
Chau, C.K., Sim, K.M.: The price of anarchy for non-atomic congestion games with symmetric cost maps and elastic demands. Operations Research Letters 31, 327–334 (2003)
Correa, J.R., Schulz, A.S., Stier-Moses, N.E.: Selfish routing in capacitated networks. Mathematics of Operations Research 29, 961–976 (2004)
Dafermos, S.C., Sparrow, F.T.: The traffic assignment problem for a general network. Journal of Research of the U.S. National Bureau of Standards 73B, 91–118 (1969)
Fotakis, D., Kontogiannis, S.C., Spirakis, P.G.: Selfish unsplittable flows. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 593–605. Springer, Heidelberg (2004)
Harker, P.T.: Multiple equilibrium behaviors of networks. Transportation Science 22, 39–46 (1988)
Hartman, G., Stampacchia, G.: On some nonlinear elliptic differential equations. Acta Mathematica 115, 271–310 (1966)
Jahn, O., Möhring, R.H., Schulz, A.S., Stier-Moses, N.E.: System-optimal routing of traffic flows with user constraints in networks with congestion. Operations Research (2005) (to appear)
Koutsoupias, E., Papadimitriou, C.H.: Worst-case equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563, pp. 404–413. Springer, Heidelberg (1999)
Milchtaich, I.: Generic uniqueness of equilibrium in large crowding games. Mathematics of Operations Research 25, 349–364 (2000)
Milchtaich, I.: Social optimality and cooperation in nonatomic congestion games. Journal of Economic Theory 114, 56–87 (2004)
Orda, A., Rom, R., Shimkin, N.: Competitive routing in multiuser communication networks. IEEE/ACM Transactions on Networking 1, 510–521 (1993)
Papadimitriou, C.H.: Algorithms, games, and the internet. In: Proceedings of the 33rd Annual ACM Symposium on Theory of Computing (STOC), Hersonissos, Greece, pp. 749–753. ACM Press, New York (2001)
Perakis, G.: The “price of anarchy” under nonlinear and asymmetric costs. In: Bienstock, D., Nemhauser, G.L. (eds.) IPCO 2004. LNCS, vol. 3064, pp. 46–58. Springer, Heidelberg (2004)
Qiu, L., Yang, Y.R., Zhang, Y., Shenker, S.: On selfish routing in internet-like environments. In: Proceedings of the 2003 Conference on Applications, Technologies, Architectures, and Protocols for Computer Communications (SIGCOMM), Karlsruhe, Germany, pp. 151–162. ACM Press, New York (2003)
Rosenthal, R.W.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)
Roughgarden, T.: The price of anarchy is independent of the network topology. Journal of Computer and System Sciences 67, 341–364 (2003)
Roughgarden, T.: Selfish routing with atomic players. In: Proceedings of the 16th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Vancouver, Canada, pp. 973–974. SIAM, Philadelphia (2005)
Roughgarden, T., Tardos, É.: How bad is selfish routing? Journal of the ACM 49, 236–259 (2002)
Roughgarden, T., Tardos, É.: Bounding the inefficiency of equilibria in nonatomic congestion games. Games and Economic Behavior 47, 389–403 (2004)
Schmeidler, D.: Equilibrium points of nonatomic games. Journal of Statistical Physics 7, 295–300 (1973)
Schulz, A.S., Stier-Moses, N.E.: On the performance of user equilibria in traffic networks. In: Proceedings of the 14th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), Baltimore, MD, pp. 86–87. SIAM, Philadelphia (2003)
Smith, M.J.: The existence, uniqueness and stability of traffic equilibria. Transportation Research 13B, 295–304 (1979)
Wardrop, J.G.: Some theoretical aspects of road traffic research. Proceedings of the Institution of Civil Engineers, Part II 1, 325–378 (1952)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Correa, J.R., Schulz, A.S., Stier-Moses, N.E. (2005). On the Inefficiency of Equilibria in Congestion Games. In: Jünger, M., Kaibel, V. (eds) Integer Programming and Combinatorial Optimization. IPCO 2005. Lecture Notes in Computer Science, vol 3509. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11496915_13
Download citation
DOI: https://doi.org/10.1007/11496915_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26199-5
Online ISBN: 978-3-540-32102-6
eBook Packages: Computer ScienceComputer Science (R0)