Asynchronous Best-Reply Dynamics
WINE '08 Proceedings of the 4th International Workshop on Internet and Network Economics
Payoff-Based Dynamics for Multiplayer Weakly Acyclic Games
SIAM Journal on Control and Optimization
Adaptive Learning in Systems of Interacting Agents
WINE '09 Proceedings of the 5th International Workshop on Internet and Network Economics
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
Mixing time and stationary expected social welfare of logit dynamics
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
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
ACM SIGecom Exchanges
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We present the first general bounds on the mixing time of logit dynamics for wide classes of strategic games. The logit dynamics describes the behaviour of a complex system whose individual components act "selfishly" and keep responding according to some partial ("noisy") knowledge of the system. In particular, we prove nearly tight bounds for potential games and games with dominant strategies. Our results show that, for potential games, the mixing time is upper and lower bounded by an "exponential" in the inverse of the noise and in the maximum potential difference. Instead, for games with dominant strategies, the mixing time cannot grow arbitrarily with the inverse of the noise. Finally, we refine our analysis for a subclass of potential games called "graphical" coordination games and we give evidence that the mixing time strongly depends on the structure of the underlying graph. Games in this class have been previously studied in Physics and, more recently, in Computer Science in the context of diffusion of new technologies.