A Collective Variational Principle Unifying Bayesian Inference, Game Theory, and Thermodynamics
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866910180644487168 |
|---|---|
| author | Bouchaffra, Djamel Ykhlef, Faycal Lebbah, Mustapha Azzag, Hanane |
| author_facet | Bouchaffra, Djamel Ykhlef, Faycal Lebbah, Mustapha Azzag, Hanane |
| contents | Collective intelligence emerges across biological, physical, and artificial systems without central coordination, yet a unifying principle governing such behaviour remains elusive. The Free Energy Principle explains how individual agents adapt through variational inference, while game theory formalises strategic interactions. Here we introduce the Game-Theoretic Free Energy Principle, a unified framework showing that multi-agent systems performing local free-energy minimisation implicitly implement a stochastic game. We prove that, under bounded rationality and local information constraints, stationary points of collective free energy correspond to approximate Nash equilibria of an induced game. Conversely, a broad class of cooperative games admits a variational representation in which equilibria arise as Gibbs distributions over coalitions, establishing a bridge between Bayesian inference and strategic interaction. To characterise higher-order effects, we introduce a free-energy formulation of the Harsanyi dividend, isolating irreducible multi-agent synergy. This yields a predictive theory of cooperation, including a falsifiable non-monotonic relationship between sensory precision and agent influence. We validate this prediction across neural, biological, and artificial multi-agent systems. These results identify a common variational principle underlying inference, thermodynamics, and game-theoretic equilibrium. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_27942 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Collective Variational Principle Unifying Bayesian Inference, Game Theory, and Thermodynamics Bouchaffra, Djamel Ykhlef, Faycal Lebbah, Mustapha Azzag, Hanane Artificial Intelligence Collective intelligence emerges across biological, physical, and artificial systems without central coordination, yet a unifying principle governing such behaviour remains elusive. The Free Energy Principle explains how individual agents adapt through variational inference, while game theory formalises strategic interactions. Here we introduce the Game-Theoretic Free Energy Principle, a unified framework showing that multi-agent systems performing local free-energy minimisation implicitly implement a stochastic game. We prove that, under bounded rationality and local information constraints, stationary points of collective free energy correspond to approximate Nash equilibria of an induced game. Conversely, a broad class of cooperative games admits a variational representation in which equilibria arise as Gibbs distributions over coalitions, establishing a bridge between Bayesian inference and strategic interaction. To characterise higher-order effects, we introduce a free-energy formulation of the Harsanyi dividend, isolating irreducible multi-agent synergy. This yields a predictive theory of cooperation, including a falsifiable non-monotonic relationship between sensory precision and agent influence. We validate this prediction across neural, biological, and artificial multi-agent systems. These results identify a common variational principle underlying inference, thermodynamics, and game-theoretic equilibrium. |
| title | A Collective Variational Principle Unifying Bayesian Inference, Game Theory, and Thermodynamics |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2604.27942 |