Pure Nash Equilibria in Player-Specific and Weighted Congestion Games
Unlike standard congestion games, weighted congestion games and congestion games with player-specific delay functions do not necessarily possess pure Nash equilibria. It is known, however, that there exist pure equilibria for both of these variants in the case of singleton congestion games, i. e., if the players’ strategy spaces contain only sets of cardinality one. In this paper, we investigate how far such a property on the players’ strategy spaces guaranteeing the existence of pure equilibria can be extended. We show that both weighted and player-specific congestion games admit pure equilibria in the case of matroid congestion games, i. e., if the strategy space of each player consists of the bases of a matroid on the set of resources. We also show that the matroid property is the maximal property that guarantees pure equilibria without taking into account how the strategy spaces of different players are interweaved. In the case of player-specific congestion games, our analysis of matroid games also yields a polynomial time algorithm for computing pure equilibria.
KeywordsNash Equilibrium Minimum Delay Strategy Space Delay Function Congestion Game
Unable to display preview. Download preview PDF.
- 1.Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. In: Proc. 47th Ann. IEEE Symp. on Foundations of Computer Science (FOCS) (to appear, 2006)Google Scholar
- 3.Fabrikant, A., Papadimitriou, C., Talwar, K.: The complexity of pure Nash equilibria. In: Proc. 36th Ann. ACM Symp. on Theory of Comput. (STOC), pp. 604–612 (2004)Google Scholar
- 5.Gairing, M., Lücking, T., Mavronicolas, M., Monien, B.: Computing nash equilibria for scheduling on restricted parallel links. In: Proc. 36th Ann. ACM Symp. on Theory of Comput (STOC), pp. 613–622 (2004)Google Scholar
- 7.Georgiou, C., Pavlides, T., Philippou, A.: Uncertainty in selfish routing. In: Proc. 20th IEEE International Parallel and Distributed Processing Symposium (IPDPS) (2006)Google Scholar
- 8.Goemans, M.X., Li, E.L., Mirrokni, V.S., Thottan, M.: Market sharing games applied to content distribution in ad-hoc networks. In: MobiHoc, pp. 55–66 (2004)Google Scholar
- 9.Ieong, S., McGrew, R., Nudelman, E., Shoham, Y., Sun, Q.: Fast and compact: A simple class of congestion games. In: 20th National Conference on Artificial Intelligence (AAAI) (2005)Google Scholar
- 12.Schrijver, A.: Combinatorial Optimization: Polyhedra and Efficiency. In: Matroids, Trees, Stable Sets, ch. 39-69, vol. B. Springer, Heidelberg (2003)Google Scholar