Abstract
Many resource sharing scenarios can be modeled as congestion games. A nice property of congestion games is that simple dynamics are guaranteed to converge to Nash equilibria. Loose bounds on the convergence time are known, but exact results are difficult to obtain in general. We investigate congestion games where the resources are homogeneous but can be player-specific. In these games, players always prefer less used resources. We derive exact conditions for the longest and shortest convergence times. We also extend the results to games on graphs, where individuals only cause congestions to their neighbors. As an example, we apply our results to study cognitive radio networks, where selfish users share wireless spectrum opportunities that are constantly changing. We demonstrate how fast the users need to be able to switch channels in order to track the time-variant channel availabilities.
This work is supported by the General Research Funds (Project Number 412509) established under the University Grant Committee of the Hong Kong Special Administrative Region, China.
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
Rosenthal, R.: A class of games possessing pure-strategy Nash equilibria. International Journal of Game Theory 2, 65–67 (1973)
Vöcking, B., Aachen, R.: Congestion games: Optimization in competition. In: Proceedings of the Second ACiD Workshop (2006)
Fabrikant, A., Papadimitriou, C., Talwar, K.: The Complexity of Pure Nash Equilibria. In: Proceedings of STOC 2004 (2005)
Fotakis, D., Kontogiannis, S., Spirakis, P.: Atomic Congestion Games Among Coalitions. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006, Part I. LNCS, vol. 4051, pp. 572–583. Springer, Heidelberg (2006)
Fotakis, D., Kaporis, A.C., Spirakis, P.G.: Atomic Congestion Games: Fast, Myopic and Concurrent. In: Monien, B., Schroeder, U.-P. (eds.) SAGT 2008. LNCS, vol. 4997, pp. 121–132. Springer, Heidelberg (2008)
Ieong, S., Mcgrew, R., Nudelman, E., Shoham, Y., Sun, Q.: Fast and Compact: A Simple Class of Congestion Games. In: Proceedings of AAAI 2005 (2005)
Ackermann, H., Röglin, H., Vöcking, B.: On the Impact of Combinatorial Structure on Congestion Games. In: Proceedings of FOCS 2006 (2006)
Law, L., Huang, J., Liu, M., Li, S.: Price of Anarchy for Cognitive MAC Games. In: Proceedings of GLOBECOM 2009 (2009)
Ahmad, S., Tekin, C., Liu, M., Southwell, R., Huang, J.: Spectrum Sharing as Spatial Congestion Games. arXiv:1011.5384v1 [cs.GT] (2010)
Southwell, R., Huang, J.: Online technical report, http://richardsouthwell.wordpress.com/technicalreport/
Wan, H., Wootton, J.: A global compositional complexity measure for biological sequences: AT-rich and GC-rich genomes encode less complex proteins. Computers and Chemistry 24, 71–94 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
About this paper
Cite this paper
Southwell, R., Huang, J. (2012). Convergence Dynamics of Resource-Homogeneous Congestion Games. In: Jain, R., Kannan, R. (eds) Game Theory for Networks. GameNets 2011. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 75. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30373-9_20
Download citation
DOI: https://doi.org/10.1007/978-3-642-30373-9_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-30372-2
Online ISBN: 978-3-642-30373-9
eBook Packages: Computer ScienceComputer Science (R0)