Abstract
We consider resource allocation games with heterogeneous users and identical resources. Most of the previous work considered cost structures with either negative or positive congestion effects. We study a cost structure that encompasses both the resource’s load and the job’s share in the resource’s activation cost.
We consider the proportional sharing rule, where the resource’s activation cost is shared among its users proportionally to their lengths. We also challenge the assumption regarding the existence of a fixed set of resources, and consider settings with an unlimited supply of resources.
We provide results with respect to equilibrium existence, computation, convergence and quality. We show that if the resource’s activation cost is shared equally among its users, a pure Nash equilibrium (NE) might not exist. In contrast, under the proportional sharing rule, a pure NE always exists, and can be computed in polynomial time. Yet, starting at an arbitrary profile of actions, best-response dynamics might not converge to a NE. Finally, we prove that the price of anarchy is unbounded and the price of stability is between 18/17 and 5/4.
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
Albers, S., Elits, S., Even-Dar, E., Mansour, Y., Roditty, L.: On Nash Equilibria for a Network Creation Game. In: SODA (2006)
Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, É., Wexler, T., Roughgarden, T.: The PoS for Network Design with Fair Cost Allocation. In: FOCS (2004)
Anshelevich, E., Dasgupta, A., Tardos, E., Wexler, T.: Near-Optimal Network Design with Selfish Agents. In: STOC (2003)
Czumaj, A., Vöcking, B.: Tight Bounds for Worst-case Equilibria. In: SODA (2002)
Epstein, A., Feldman, M., Mansour, Y.: Strong Equilibrium in Cost Sharing Connection Games. In: ACMEC (2007)
Even-Dar, E., Mansour, Y.: Fast Convergence of Selfish Rerouting. In: SODA (2005)
Fabrikant, A., Luthra, A., Maneva, E., Papadimitriou, C., Shenker, S.: On a Network Creation Game. In: PODC (2003)
Feigenbaum, J., Papadimitriou, C., Shenker, S.: Sharing the Cost of Multicast Transmissions. J. of Computer and System Sciences 63, 21–41 (2001)
Feldman, M., Tamir, T.: Conflicting Congestion Effects in Resource Allocation Games, http://www.faculty.idc.ac.il/tami/Papers/coco.pdf
Fotakis, D., Kontogiannis, S., Mavronicolas, M., Spiraklis, 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. Springer, Heidelberg (2002)
Graham, R.: Bounds on Multiprocessing Timing Anomalies. SIAM J. Appl. Math. 17, 263–269 (1969)
Herzog, S., Shenker, S., Estrin, D.: Sharing the ”Cost” of Multicast Trees: An Axiomatic Analysis. IEEE/ACM Transactions on Networking (1997)
Koutsoupias, E., Papadimitriou, C.H.: Worst-case Equilibria. In: Meinel, C., Tison, S. (eds.) STACS 1999. LNCS, vol. 1563. Springer, Heidelberg (1999)
Monderer, D., Shapley, L.S.: Potential Games. Games and Economic Behavior 14, 124–143 (1996)
Moulin, H., Shenker, S.: Serial Cost Sharing. Econometrica 60, 1009–1037 (1992)
Moulin, H., Shenker, S.: Strategyproof Sharing of Submodular Costs: Budget Balance Versus Efficiency. Journal of Economic Theory 18, 511–533 (2001)
Nisan, N., Roughgarden, T., Tardos, E., Vazirani, V.V.: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)
Papadimitriou, C.: Algorithms, Games, and the Internet. In: STOC (2001)
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. In: STOC (2002)
Roughgarden, T., Tardos, E.: How Bad is Selfish Routing? Journal of the ACM 49(2), 236–259 (2002)
Vetta, A.R.: Nash Equilibria in Competitive Societies with Applications to Facility Location, Traffic Routing and Auctions. In: FOCS (2002)
Vöcking, B.: Selfish Load Balancing. In: Algorithmic Game Theory. Cambridge University Press, Cambridge (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Feldman, M., Tamir, T. (2008). Conflicting Congestion Effects in Resource Allocation Games. In: Papadimitriou, C., Zhang, S. (eds) Internet and Network Economics. WINE 2008. Lecture Notes in Computer Science, vol 5385. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-92185-1_19
Download citation
DOI: https://doi.org/10.1007/978-3-540-92185-1_19
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-92184-4
Online ISBN: 978-3-540-92185-1
eBook Packages: Computer ScienceComputer Science (R0)