The price of anarchy of finite congestion games
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Sink Equilibria and Convergence
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
The complexity of game dynamics: BGP oscillations, sink equilibria, and beyond
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Settling the complexity of computing two-player Nash equilibria
Journal of the ACM (JACM)
The Price of Stability for Network Design with Fair Cost Allocation
SIAM Journal on Computing
The Complexity of Computing a Nash Equilibrium
SIAM Journal on Computing
On the Inefficiency Ratio of Stable Equilibria in Congestion Games
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
Convergence to Equilibrium in Local Interaction Games
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
On the equilibria of alternating move games
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Convergence to equilibrium of logit dynamics for strategic games
Proceedings of the twenty-third annual ACM symposium on Parallelism in algorithms and architectures
Metastability of logit dynamics for coordination games
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Stability and metastability of the logit dynamics of strategic games
FUN'12 Proceedings of the 6th international conference on Fun with Algorithms
Decentralized dynamics for finite opinion games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
Logit dynamics: a model for bounded rationality
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We study logit dynamics [Blume, Games and Economic Behavior, 1993] for strategic games. At every stage of the game a player is selected uniformly at random and she plays according to a noisy best-response dynamics where the noise level is tuned by a parameter β. Such a dynamics defines a family of ergodic Markov chains, indexed by β, over the set of strategy profiles. Our aim is twofold: On the one hand, we are interested in the expected social welfare when the strategy profiles are random according to the stationary distribution of the Markov chain, because we believe it gives a meaningful description of the long-term behavior of the system. On the other hand, we want to estimate how long it takes, for a system starting at an arbitrary profile and running the logit dynamics, to get close to the stationary distribution; i.e., the mixing time of the chain. In this paper we study the stationary expected social welfare for the 3-player congestion game that exhibits the worst Price of Anarchy [Christodoulou and Koutsoupias, STOC'05], for 2-player coordination games (the same class of games studied by Blume), and for a simple n-player game. For all these games, we give almost-tight upper and lower bounds on the mixing time of logit dynamics.