Abstract
We study the model of resource allocation games with conflicting congestion effects introduced by Feldman and Tamir (2012). In this model, an agent’s cost consists of its resource’s load (which increases with congestion) and its share in the resource’s activation cost (which decreases with congestion). The current work studies the convergence rate of best-response dynamics (BRD) in the case of homogeneous agents. Even within this simple setting, interesting phenomena arise. We show that, in contrast to standard congestion games with identical jobs and resources, the convergence rate of BRD under conflicting congestion effects might be super-linear in the number of jobs. Nevertheless, a specific form of BRD is proposed, which is guaranteed to converge in linear time.
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References
Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. In: FOCS 2006, pp. 613–622 (2006)
Anshelevich, E., Dasgupta, A., Kleinberg, J.M., Tardos, É., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. In: FOCS 2004, pp. 295–304 (2004)
Awerbuch, B., Azar, Y., Epstein, A., Mirrokni, V.S., Skopalik, A.: Fast convergence to nearly optimal solutions in potential games. In: ACMEC 2008, pp. 264–273 (2008)
Chen, B., Gürel, S.: Efficiency analysis of load balancing games with and without activation costs. Journal of Scheduling 15(2) (2011)
Chien, S., Sinclair, A.: Convergence to approximate Nash equilibria in congestion games. In: SODA 2007, pp. 169–178 (2007)
Epstein, A., Feldman, M., Mansour, Y.: Strong equilibrium in cost sharing connection games. Games and Economic Behavior 67(1) (2009)
Even-Dar, E., Kesselman, A., Mansour, Y.: Convergence Time to Nash Equilibria. In: Baeten, J.C.M., Lenstra, J.K., Parrow, J., Woeginger, G.J. (eds.) ICALP 2003. LNCS, vol. 2719, pp. 502–513. Springer, Heidelberg (2003)
Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure Nash equilibria. In: STOC 2004, pp. 604–612 (2004)
Feldman, M., Tamir, T.: Conflicting congestion effects in resource allocation games. Operations Research 60(3), 529–540 (2012)
Feldman, M., Tamir, T.: Conflicting congestion effects in resource allocation games. Full version, http://www.faculty.idc.ac.il/tami/Papers/BRDcoco.pdf
Fotakis, D., Kontogiannis, S., Koutsoupias, E., Mavronicolas, M., Spirakis, P.: The Structure and Complexity of Nash Equilibria for a Selfish Routing Game. In: Widmayer, P., Triguero, F., Morales, R., Hennessy, M., Eidenbenz, S., Conejo, R. (eds.) ICALP 2002. LNCS, vol. 2380, pp. 123–519. Springer, Heidelberg (2002)
Fotakis, D.: Congestion games with linearly independent paths: convergence time and price of anarchy. Theory Comput. Syst. 47(1), 113–136 (2010)
Hoefer, M., Skopalik, A.: Stability and Convergence in Selfish Scheduling with Altruistic Agents. In: Leonardi, S. (ed.) WINE 2009. LNCS, vol. 5929, pp. 616–622. Springer, Heidelberg (2009)
Ieong, S., Mcgrew, R., Nudelman, E., Shoham, Y., Sun, Q.: Fast and Compact: A simple class of congestion games. In: AAAI 2005, pp. 489–494 (2005)
Johari, R., Kumar, S.: Congestible services and network effects. In: EC 2010, pp. 93–94 (2010)
Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Computer Science Review 3(2), 65–69 (2009)
Monderer, D., Shapley, L.S.: Potential games. Games and Economic Behavior 14, 124–143 (1996)
Papadimitriou, C.: Algorithms, games, and the Internet. In: STOC 2001, pp. 749–753 (2001)
Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibria. International Journal of Game Theory 2, 65–67 (1973)
Roughgarden, T., Tardos, E.: How bad is selfish routing? Journal of the ACM 49(2), 236–259 (2002)
Syrgkanis, V.: The Complexity of Equilibria in Cost Sharing Games. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 366–377. Springer, Heidelberg (2010)
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Feldman, M., Tamir, T. (2012). Convergence of Best-Response Dynamics in Games with Conflicting Congestion Effects. In: Goldberg, P.W. (eds) Internet and Network Economics. WINE 2012. Lecture Notes in Computer Science, vol 7695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-35311-6_38
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DOI: https://doi.org/10.1007/978-3-642-35311-6_38
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