Journal of Computer and System Sciences - 26th IEEE Conference on Foundations of Computer Science, October 21-23, 1985
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Price of Routing Unsplittable Flow
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the Impact of Combinatorial Structure on Congestion Games
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Algorithms for pure Nash equilibria in weighted congestion games
Journal of Experimental Algorithmics (JEA)
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Inapproximability of pure nash equilibria
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
The Speed of Convergence in Congestion Games under Best-Response Dynamics
ICALP '08 Proceedings of the 35th international colloquium on Automata, Languages and Programming, Part I
Congestion Games with Linearly Independent Paths: Convergence Time and Price of Anarchy
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
On the price of anarchy and stability of correlated equilibria of linear congestion games,,
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Symmetry in network congestion games: pure equilibria and anarchy cost
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
Tight bounds for selfish and greedy load balancing
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Convergence and approximation in potential games
Theoretical Computer Science
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We investigate the approximation ratio of the solutions achieved after a one-round walk in linear congestion games. We consider the social functions ${\mathrm{S}\textsc{um}}$, defined as the sum of the players' costs, and ${\mathrm{M}\textsc{ax}}$, defined as the maximum cost per player, as a measure of the quality of a given solution. For the social function ${\mathrm{S}\textsc{um}}$ and one-round walks starting from the empty strategy profile, we close the gap between the upper bound of $2+\sqrt{5}\approx 4.24$ given in [8] and the lower bound of 4 derived in [4] by providing a matching lower bound whose construction and analysis require non-trivial arguments. For the social function ${\mathrm{M}\textsc{ax}}$, for which, to the best of our knowledge, no results were known prior to this work, we show an approximation ratio of $\Theta(\sqrt[4]{n^3})$ (resp. $\Theta(n\sqrt{n})$), where n is the number of players, for one-round walks starting from the empty (resp. an arbitrary) strategy profile.