# Mixing Time and Stationary Expected Social Welfare of Logit Dynamics

@article{Auletta2013MixingTA, title={Mixing Time and Stationary Expected Social Welfare of Logit Dynamics}, author={Vincenzo Auletta and Diodato Ferraioli and Francesco Pasquale and Giuseppe Persiano}, journal={Theory of Computing Systems}, year={2013}, volume={53}, pages={3-40} }

We study logit dynamics (Blume in Games Econ. Behav. 5:387–424, 1993) for strategic games. This dynamics works as follows: at every stage of the game a player is selected uniformly at random and she plays according to a noisy best-response 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. We believe that the stationary distribution of these Markov chains gives a meaningful description of…

## 25 Citations

### Stability and Metastability of the Logit Dynamics of Strategic Games

- EconomicsFUN
- 2012

It is shown that for ptential games, the mixing time is related to properties of the potential landscape and thus it is proposed to look at metastable distributions for such systems.

### Metastability of Logit Dynamics for Coordination Games

- EconomicsAlgorithmica
- 2017

A quantitative definition of “metastable probability distributions” for a Markov chain is given and the metastability of the logit dynamics for some classes of coordination games is studied.

### Metastability of Logit Dynamics for Coordination Games (full version)

- Economics
- 2011

Logit Dynamics [Blume, Games and Economic Behavior, 1993] is a randomized best response dynamics for strategic games: at every time step a player is selected uniformly at random and she chooses a new…

### Reversibility and Mixing Time for Logit Dynamics with Concurrent Updates

- Economics, MathematicsArXiv
- 2012

The dynamics where at every time step every player simultaneously updates her strategy according to the logit choice function is called the “all-logit”, as opposed to the classical “one-logIt” dynamics, which is a subclass of potential games.

### Logit Dynamics with Concurrent Updates for Local Interaction Potential Games

- EconomicsAlgorithmica
- 2014

It is proved that local interaction potential games characterize the class of games for which the all-logit dynamics is reversible, and it is shown that the mixing time of the all"-logit" dynamics has the same twofold behavior that has been highlighted in the case of the one- logit.

### Metastability of the Logit Dynamics for Asymptotically Well-Behaved Potential Games

- Mathematics, EconomicsACM Trans. Algorithms
- 2019

It is proved that every potential game, for which the behavior of the logit dynamics is not chaotic as n increases, admits distributions stable for a super-polynomial number of steps in n no matter the players’ irrationality and the starting profile of the dynamics.

### Convergence to Equilibrium of Logit Dynamics for Strategic Games

- MathematicsSPAA '11
- 2011

The first general bounds on the mixing time of the Markov chain associated to the logit dynamics for wide classes of strategic games are presented, and nearly tight bounds for potential games and games with dominant strategies are proved.

### Metastability of Asymptotically Well-Behaved Potential Games

- Economics
- 2012

It is proved that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics, which can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential.

### Metastability of Asymptotically Well-Behaved Potential Games - (Extended Abstract)

- EconomicsMFCS
- 2015

It is proved that any such game admits distributions which are metastable no matter the level of noise present in the system, and the starting profile of the dynamics, which can be quickly reached if the rationality level is not too big when compared to the inverse of the maximum difference in potential.

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