The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Bounds for the convergence rate of randomized local search in a multiplayer load-balancing game
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Distributed selfish load balancing
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Fast and compact: a simple class of congestion games
AAAI'05 Proceedings of the 20th national conference on Artificial intelligence - Volume 2
Convergence time to Nash equilibria
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Pure nash equilibria in player-specific and weighted congestion games
WINE'06 Proceedings of the Second international conference on Internet and Network Economics
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We initiate studying the convergence time to Nash equilibria in player-specific singleton congestion games. We consider simple games that have natural representations as graphs as we assume that each player chooses between two resources. We are not able to present an analysis for general graphs. However, we present first results for interesting classes of graphs. For the class of games that are represented as trees, we show that every best-response schedule terminates after O(n2) steps. We also consider games that are represented as circles. We show that deterministic best response schedules may cycle, whereas the random best response schedule, which selects the next player to play a best response uniformly at random, terminates after O(n2) steps in expectation. These results imply that in player-specific congestion games in which each player chooses between two resources, and each resource is allocated by at most two players, the random best response schedule terminates quickly. Our analysis reveals interesting relationships between random walks on lines and the random best response schedule.