The logit-response dynamics

Alós–Ferrer, Carlos; Netzer, Nick

doi:10.1016/j.geb.2009.08.004

Cited by 171 publications

(147 citation statements)

References 28 publications

(49 reference statements)

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“…Nonetheless, log-linear learning has received significant research attention [1,2,6,9,10,15,32]. These results range from analyzing convergence rates [6,25] to the necessity of the structural requirements [1].…”

Section: Introductionmentioning

confidence: 99%

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Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation

Marden

Shamma

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

134

306

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Log-linear learning is a learning algorithm with equilibrium selection properties. Log-linear learning provides guarantees on the percentage of time that the joint action profile will be at a potential maximizer in potential games. The traditional analysis of log-linear learning has centered around explicitly computing the stationary distribution. This analysis relied on a highly structured setting: i) players' utility functions constitute a potential game, ii) players update their strategies one at a time, which we refer to as asynchrony, iii) at any stage, a player can select any action in the action set, which we refer to as completeness, and iv) each player is endowed with the ability to assess the utility he would have received for any alternative action provided that the actions of all other players remain fixed. Since the appeal of log-linear learning is not solely the explicit form of the stationary distribution, we seek to address to what degree one can relax the structural assumptions while maintaining that only potential function maximizers are the stochastically stable action profiles. In this paper, we introduce slight variants of log-linear learning to include both synchronous updates and incomplete action sets. In both settings, we prove that only potential function maximizers are stochastically stable. Furthermore, we introduce a payoff-based version of log-linear learning, in which players are only aware of the utility they received and the action that they played. Note that log-linear learning in its original form is not a payoff-based learning algorithm. In payoff-based log-linear learning, we also prove that only potential maximizers are stochastically stable. The key enabler for these results is to change the focus of the analysis away from deriving the explicit form of the stationary distribution of the learning process towards characterizing the stochastically stable states. The resulting analysis uses the theory of resistance trees for regular perturbed Markov decision processes, thereby allowing a relaxation of the aforementioned structural assumptions.

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Section: Introductionmentioning

confidence: 99%

“…These results range from analyzing convergence rates [6,25] to the necessity of the structural requirements [1]. In particular, [1] demonstrates that if the structural requirements of (i) and (ii) are relaxed arbitrarily, then the equilibrium selection properties of log-linear learning are no longer guaranteed.…”

Section: Introductionmentioning

confidence: 99%

Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation

Marden

Shamma

2010

2010 48th Annual Allerton Conference on Communication, Control, and Computing (Allerton)

134

306

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“…Our next result focuses on the learning algorithm log-linear learning (Alos-Ferrer & Netzer, 2010;Blume, 1993Blume, , 1997Marden & Shamma, 2012;Shah & Shin, 2010). In potential games, log-linear learning provides guarantees on the percentage of time that the joint action profile will be at a maximizer of the potential function.…”

Section: Introductionmentioning

confidence: 99%

State based potential games

2012

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“…The most prominent implementation of this assumption is the logit response model (Blume, 1993). Except under certain symmetry/regularity conditions (Blume, 2003), costsensitive deviations have been shown to imply different convergence predictions than constant errors (Young, 1998;Blume, 2003;Myatt and Wallace, 2004;Alós-Ferrer and Netzer, 2010), particularly with regard to convergence times (Ellison, 1993;Young, 1998Young, , 2011a. 2 A third set of deviation assumptions stems from payoff-based learning models Mas-Colell, 2003, 2006;Foster and Young, 2006;Young, 2009), which share the assumption that agents adjust their behavior based on trial-and-error heuristics rather than bestresponse considerations.…”

Section: Competing Deviation Assumptionsmentioning

confidence: 99%

A Behavioral Study of 'Noise' in Coordination Games

Maes

Nax

2014

SSRN Journal

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Abstract'Noise' in this study, in the sense of evolutionary game theory, refers to deviations from prevailing behavioral rules. Analyzing data from a laboratory experiment on coordination in networks, we tested 'what kind of noise' is supported by behavioral evidence. This empirical analysis complements a growing theoretical literature on 'how noise matters' for equilibrium selection. We find that the vast majority of decisions (96%) constitute myopic best responses, but deviations continue to occur with probabilities that are sensitive to their costs, that is, less frequent when implying larger payoff losses relative to the myopic best response. In addition, deviation rates vary with patterns of realized payoffs that are related to trial-and-error behavior. While there is little evidence that deviations are clustered in time or space, there is evidence of individual heterogeneity.

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The logit-response dynamics

Cited by 171 publications

References 28 publications

Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation

Revisiting log-linear learning: Asynchrony, completeness and payoff-based implementation

State based potential games

A Behavioral Study of 'Noise' in Coordination Games

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