The Price of Stability for Network Design with Fair Cost Allocation
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Convergence to approximate Nash equilibria in congestion games
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Regret minimization and the price of total anarchy
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 Price of Stochastic Anarchy
SAGT '08 Proceedings of the 1st International Symposium on Algorithmic Game Theory
Multiplicative updates outperform generic no-regret learning in congestion games: extended abstract
Proceedings of the forty-first annual ACM symposium on Theory of computing
Convergence to Equilibrium in Local Interaction Games
FOCS '09 Proceedings of the 2009 50th Annual IEEE Symposium on Foundations of Computer Science
Tight bounds for selfish and greedy load balancing
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Mixing time and stationary expected social welfare of logit dynamics
SAGT'10 Proceedings of the Third international conference on Algorithmic game theory
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
Nash equilibria with minimum potential in undirected broadcast games
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Decentralized dynamics for finite opinion games
SAGT'12 Proceedings of the 5th international conference on Algorithmic Game Theory
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Price of anarchy and price of stability are the primary notions for measuring the efficiency (i.e. the social welfare) of the outcome of a game. Both of these notions focus on extreme cases: one is defined as the inefficiency ratio of the worst-case equilibrium and the other as the best one. Therefore, studying these notions often results in discovering equilibria that are not necessarily the most likely outcomes of the dynamics of selfish and non-coordinating agents.The current paper studies the inefficiency of the equilibria that are most stable in the presence of noise. In particular, we study two variations of non-cooperative games: atomic congestion games and selfish load balancing. The noisy best-response dynamics in these games keeps the joint action profile around a particular set of equilibria that minimize the potential function. The inefficiency ratio in the neighborhood of these "stable" equilibria is much better than the price of anarchy. Furthermore, the dynamics reaches these equilibria in polynomial time.Our observations show that in the game environments where a small noise is present, the system as a whole works better than what a pessimist may predict. They also suggest that in congestion games, introducing a small noise in the payoff of the agents may improve the social welfare.