Fast convergence to nearly optimal solutions in potential games
Proceedings of the 9th ACM conference on Electronic commerce
Efficient coordination mechanisms for unrelated machine scheduling
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Concurrent imitation dynamics in congestion games
Proceedings of the 28th ACM symposium on Principles of distributed computing
Performances of One-Round Walks in Linear Congestion Games
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
On Best Response Dynamics in Weighted Congestion Games with Polynomial Delays
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Convergence and approximation in potential games
Theoretical Computer Science
Dynamics of profit-sharing games
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume One
On the impact of fair best response dynamics
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
A theoretical examination of practical game playing: lookahead search
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
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We investigate the speed of convergence of congestion games with linear latency functions under best response dynamics. Namely, we estimate the social performance achieved after a limited number of rounds, during each of which every player performs one best response move. In particular, we show that the price of anarchy achieved after k rounds, defined as the highest possible ratio among the total latency cost, that is the sum of all players latencies, and the minimum possible cost, is $O(\sqrt[2^{k-1}] {n})$, where n is the number of players. For constant values of k such a bound asymptotically matches the $\Omega(\sqrt[2^{k-1}] {n}/k)$ lower bound that we determine as a refinement of the one in [7]. As a consequence, we prove that order of loglogn rounds are not only necessary, but also sufficient to achieve a constant price of anarchy, i.e. comparable to the one at Nash equilibrium. This result is particularly relevant, as reaching an equilibrium may require a number of rounds exponential in n. We then provide a new lower bound of $\Omega(\sqrt[2^k-1] {n})$ for load balancing games, that is congestion games in which every strategy consists of a single resource, thus showing that a number of rounds proportional to loglogn is necessary and sufficient also under such a restriction.Our results thus solve the important left open question of the polynomial speed of convergence of linear congestion games to constant factor solutions.