Constructive Linear Time Algorithms for Small Cutwidth and Carving-Width
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
Path coupling: A technique for proving rapid mixing in Markov chains
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
The complexity of pure Nash equilibria
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Improved equilibria via public service advertising
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Social and Economic Networks
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
Approximating pure nash equilibrium in cut, party affiliation, and satisfiability games
Proceedings of the 11th ACM conference on Electronic commerce
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
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
How Bad is Forming Your Own Opinion?
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Metastability of logit dynamics for coordination games
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
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Game theory studies situations in which strategic players can modify the state of a given system, due to the absence of a central authority. Solution concepts, such as Nash equilibrium, are defined to predict the outcome of such situations. In the spirit of the field, we study the computation of solution concepts by means of decentralized dynamics. These are algorithms in which players move in turns to improve their own utility and the hope is that the system reaches an "equilibrium" quickly. We study these dynamics for the class of opinion games, recently introduced by [1]. These are games, important in economics and sociology, that model the formation of an opinion in a social network. We study best-response dynamics and show that the convergence to Nash equilibria is polynomial in the number of players. We also study a noisy version of best-response dynamics, called logit dynamics, and prove a host of results about its convergence rate as the noise in the system varies. To get these results, we use a variety of techniques developed to bound the mixing time of Markov chains, including coupling, spectral characterizations and bottleneck ratio.