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2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06) (2006)
Berkeley, California
Oct. 21, 2006 to Oct. 24, 2006
ISSN: 0272-5428
ISBN: 0-7695-2720-5
pp: 613-622
Heiner Ackermann , RWTH Aachen, Germany
Heiko Roglin , RWTH Aachen, Germany
Berthold Vocking , RWTH Aachen, Germany
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, 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 can 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 can show that network congestion games are PLS-complete for directed and undirected networks even in case of linear latency functions
combinatorial mathematics, convergence, game theory, resource allocation

H. Ackermann, H. Roglin and B. Vocking, "On the Impact of Combinatorial Structure on Congestion Games," 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06)(FOCS), Berkeley, California, 2007, pp. 613-622.
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