Heiner Ackermann
Heiko Röglin
Abstract
We study the impact of combinatorial structure in congestion games on the complexity of computing pure Nash equilibria and the convergence time of best response sequences. In particular, we investigate which properties of the strategy spaces of individual players ensure a polynomial convergence time. We show that if the strategy space of each player consists of the bases of a matroid over the set of resources, then the lengths of all best response sequences are polynomially bounded in the number of players and resources. We also prove that this result is tight, that is, the matroid property is a necessary and sufficient condition on the players' strategy spaces for guaranteeing polynomial-time convergence to a Nash equilibrium.
In addition, we present an approach that enables us to devise hardness proofs for various kinds of combinatorial games, including first results about the hardness of market sharing games and congestion games for overlay network design. Our approach also yields a short proof for the PLS-completeness of network congestion games. In particular, we show that network congestion games are PLS-complete for directed and undirected networks even in case of linear latency functions.
- Ackermann, H., Röglin, H., and Vöcking, B. 2006. Pure Nash equilibria in player-specific and weighted congestion games. In Proceedings of the 2nd International Workshop on Internet and Network Economics (WINE). Lecture Notes in Computer Science, vol. 4286. Springer-Verlag, New York, 50--61. Google Scholar
Digital Library
- Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., and Roughgarden, T. 2004. The price of stability for network design with fair cost allocation. In Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE Computer Society Press, Los Alamitos, CA, 295--304. Google ScholarDigital Library
- Anshelevich, E., Dasgupta, A., Tardos, E., and Wexler, T. 2003. Near-optimal network design with selfish agents. In Proceedings of the 35th Annual ACM Symposium on Theory of Computing (STOC). ACM, New York, 511--520. Google ScholarDigital Library
- Chakrabarty, D., Mehta, A., and Nagarajan, V. 2005. Fairness and optimality in congestion games. In Proceedings of the 6th ACM Conference on Electronic Commerce. ACM, New York, 52--57. Google ScholarDigital Library
- Fabrikant, A., Papadimitriou, C. H., and Talwar, K. 2004. The complexity of pure Nash equilibria. In Proceedings of the 36th Annual ACM Symposium on Theory of Computing (STOC). ACM, New York, 604--612. Google ScholarDigital Library
- Floren, P., and Orponen, P. 1994. Complexity issues in discrete Hopfield networks. Department of Computer Science, University of Helsinki, Helsinki, Finland, Tech. Rep. A-1994-4.Google Scholar
- Goemans, M. X., Li, E. L., Mirrokni, V. S., and Thottan, M. 2004. Market sharing games applied to content distribution in ad-hoc networks. In Proceedings of the 5th ACM International Symposium on Mobile Ad Hoc Networking and Computing (MobiHoc). ACM, New York, 55--66. Google ScholarDigital Library
- Ieong, S., McGrew, R., Nudelman, E., Shoham, Y., and Sun, Q. 2005. Fast and compact: A simple class of congestion games. In Proceedings of the 20th National Conference on Artificial Intelligence (AAAI). AAAI Press, Menlo Park, CA, 489--494. Google ScholarDigital Library
- Johnson, D. S., Papadimitriou, C. H., and Yannakakis, M. 1988. How easy is local search? J. Comput. Syst. Sci. 37, 1, 79--100. Google ScholarDigital Library
- Mirrokni, V. S. 2005. Approximation algorithms for distributed and selfish agents. Ph.D. dissertation, Massachusetts Institute of Technology. Google ScholarDigital Library
- Orponen, P. 1997. Computing with truly asynchronous threshold logic networks. Theoret. Comput. Sci. 174, 1--2, 123--136. Google ScholarDigital Library
- Poljak, S. 1995. Integer linear programs and local search for max-cut. SIAM J. Comput. 24, 4, 822--839. Google ScholarDigital Library
- Rosenthal, R. W. 1973. A class of games possessing pure-strategy Nash equilibria. Int. J. Game Theory 2, 65--67.Google ScholarDigital Library
- Schäffer, A. A., and Yannakakis, M. 1991. Simple local search problems that are hard to solve. SIAM J. Comput. 20, 1, 56--87. Google ScholarDigital Library
- Schrijver, A. 2003. Combinatorial Optimization: Polyhedra and Efficiency. Springer. Volume B, Matroids, Trees, Stable Sets, Chapters 39--69.Google Scholar
- Stoica, I., Adkins, D., Zhuang, S., Shenker, S., and Surana, S. 2004. Internet indirection infrastructure. IEEE/ACM Trans. Netw. 12, 2, 205--218. Google ScholarDigital Library
- Werneck, R. F., and Setubal, J. C. 2000. Finding minimum congestion spanning trees. ACM J. Exper. Alg. 5, 11. Google ScholarDigital Library
Index Terms
- On the impact of combinatorial structure on congestion games
Recommendations
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 ...
Pure Nash equilibria in restricted budget games
In budget games, players compete over resources with finite budgets. For every resource, a player has a specific demand and as a strategy, he chooses a subset of resources. If the total demand on a resource does not exceed its budget, the utility of ...
Congestion games with mixed objectives
We study a new class of games which generalizes congestion games and its bottleneck variant. We introduce congestion games with mixed objectives to model network scenarios in which players seek to optimize for latency and bandwidths alike. We ...
Comments