The two kinds of free energy and the Bayesian revolution

Gottwald, Sebastian; Braun, Daniel A.

doi:10.1371/journal.pcbi.1008420

Cited by 31 publications

(32 citation statements)

References 102 publications

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“…This is not only in line with the quantal response equilibrium prediction, but also agrees with previous experimental results [31] that have shown that cooperation does not arise as a stable solution during haptic coupling, but only in cognitive versions of the Prisoner's Dilemma involving conscious deliberation. Our current study adds to this previous line of research by highlighting the importance of taking into account limited information processing capabilities due to bounded rationality and how to capture these using information constraints [45][46][47][48].…”

Section: Discussionmentioning

confidence: 87%

Bounded rational response equilibria in human sensorimotor interactions

2021

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The Nash equilibrium is one of the most central solution concepts to study strategic interactions between multiple players and has recently also been shown to capture sensorimotor interactions between players that are haptically coupled. While previous studies in behavioural economics have shown that systematic deviations from Nash equilibria in economic decision-making can be explained by the more general quantal response equilibria, such deviations have not been reported for the sensorimotor domain. Here we investigate haptically coupled dyads across three different sensorimotor games corresponding to the classic symmetric and asymmetric Prisoner's Dilemma, where the quantal response equilibrium predicts characteristic shifts across the three games, although the Nash equilibrium stays the same. We find that subjects exhibit the predicted deviations from the Nash solution. Furthermore, we show that taking into account subjects' priors for the games, we arrive at a more accurate description of bounded rational response equilibria that can be regarded as a quantal response equilibrium with non-uniform prior. Our results suggest that bounded rational response equilibria provide a general tool to explain sensorimotor interactions that include the Nash equilibrium as a special case in the absence of information processing limitations.

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Section: Discussionmentioning

confidence: 87%

Bounded rational response equilibria in human sensorimotor interactions

2021

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“…Another alternative without explicitly initializing the priors this way, would be to conceptualize the minimization of the trial-by-trial deviation as minimizing the information difference between each action and the marginal distribution over actions given by the average behavior. Such an implicit information penalization of action policies can be regarded as a form of bounded rational decision-making, where decision-makers trade off between utility and information costs that are required to achieve a certain level of precision [45][46][47] . Such information costs have been previously suggested to model costs of motor planning and abstraction 48,49 .…”

Section: Discussionmentioning

confidence: 99%

Nash equilibria in human sensorimotor interactions explained by Q-Learning

Lindig-León

Schmid

Braun

2021

Preprint

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The Nash equilibrium concept has previously been shown to be an important tool to understand human sensorimotor interactions, where different actors vie for minimizing their respective effort while engaging in a multi-agent motor task. However, it is not clear how such equilibria are reached. Here, we compare different reinforcement learning models based on haptic feedback to human behavior in sensorimotor versions of three classic games, including the Prisoner's Dilemma, and the symmetric and asymmetric matching pennies games. We find that a discrete analysis that reduces the continuous sensorimotor interaction to binary choices as in classical matrix games does not allow to distinguish between the different learning algorithms, but that a more detailed continuous analysis with continuous formulations of the learning algorithms and the game-theoretic solutions affords different predictions. In particular, we find that Q-learning with intrinsic costs that disfavor deviations from average behavior explains the observed data best, even though all learning algorithms equally converge to admissible Nash equilibrium solutions. We therefore conclude that it is important to study different learning algorithms for understanding sensorimotor interactions, as such behavior cannot be inferred from a game-theoretic analysis alone, that simply focuses on the Nash equilibrium concept, as different learning algorithms impose preferences on the set of possible equilibrium solutions due to the inherent learning dynamics.

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“…MacKay [10], and, for a comparison between the free energy principle and Bayesian inference, cf. Gottwald and Brown [28].…”

Section: Variational Bayesian Inferencementioning

confidence: 99%

Information and Self-Organization II: Steady State and Phase Transition

Haken

Portugali

2021

Entropy

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This paper starts from Schrödinger’s famous question “what is life” and elucidates answers that invoke, in particular, Friston’s free energy principle and its relation to the method of Bayesian inference and to Synergetics 2nd foundation that utilizes Jaynes’ maximum entropy principle. Our presentation reflects the shift from the emphasis on physical principles to principles of information theory and Synergetics. In view of the expected general audience of this issue, we have chosen a somewhat tutorial style that does not require special knowledge on physics but familiarizes the reader with concepts rooted in information theory and Synergetics.

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The two kinds of free energy and the Bayesian revolution

Cited by 31 publications

References 102 publications

Bounded rational response equilibria in human sensorimotor interactions

Bounded rational response equilibria in human sensorimotor interactions

Nash equilibria in human sensorimotor interactions explained by Q-Learning

Information and Self-Organization II: Steady State and Phase Transition

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