Differential equations and dynamical systems
Differential equations and dynamical systems
The weighted majority algorithm
Information and Computation
Fast convergence of selfish rerouting
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Fast convergence to Wardrop equilibria by adaptive sampling methods
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Regret minimization and the price of total anarchy
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Intrinsic robustness of the price of anarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
Algorithmic Game Theory: A Snapshot
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Load balancing without regret in the bulletin board model
Proceedings of the 28th ACM symposium on Principles of distributed computing
On the Inefficiency Ratio of Stable Equilibria in Congestion Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Opportunistic spectrum access with multiple users: learning under competition
INFOCOM'10 Proceedings of the 29th conference on Information communications
On learning algorithms for nash equilibria
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
Distributed selfish load balancing on networks
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Intrinsic robustness of the price of anarchy
Communications of the ACM
LP-Based covering games with low price of anarchy
WINE'12 Proceedings of the 8th international conference on Internet and Network Economics
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We study the outcome of natural learning algorithms in atomic congestion games. Atomic congestion games have a wide variety of equilibria often with vastly differing social costs. We show that in almost all such games, the well-known multiplicative-weights learning algorithm results in convergence to pure equilibria. Our results show that natural learning behavior can avoid bad outcomes predicted by the price of anarchy in atomic congestion games such as the load-balancing game introduced by Koutsoupias and Papadimitriou, which has super-constant price of anarchy and has correlated equilibria that are exponentially worse than any mixed Nash equilibrium. Our results identify a set of mixed Nash equilibria that we call weakly stable equilibria. Our notion of weakly stable is defined game-theoretically, but we show that this property holds whenever a stability criterion from the theory of dynamical systems is satisfied. This allows us to show that in every congestion game, the distribution of play converges to the set of weakly stable equilibria. Pure Nash equilibria are weakly stable, and we show using techniques from algebraic geometry that the converse is true with probability 1 when congestion costs are selected at random independently on each edge (from any monotonically parametrized distribution). We further extend our results to show that players can use algorithms with different (sufficiently small) learning rates, i.e. they can trade off convergence speed and long term average regret differently.