Strategic Structure of Neural Competition Games: Potentials, Beliefs, Plasticity, Risk, Heterogeneous Mean Fields,Identifiability and Rational Inattention

This theoretical paper expands a prefrontal–limbic brain interaction model by building seven advanced mathematical layers onto a framework of stochastic differential games with long-memory noise and quantal-response equilibrium. The first three layers focus on systemic stability and learning: they establish that the game behaves as an exact potential game under specific geometric symmetries, show that players can calculate equilibria using Kalman filters under partial visibility, and model slow synaptic changes (plasticity) using an averaged differential equation that remains stable until the system undergoes a sudden transition or "metastable escape."The remaining four layers extend the model into decision-making constraints, scale, and estimation boundaries. The authors prove that risk-sensitive costs are mathematically equivalent to robust control under uncertainty, derive how massive networks of diverse neurons behave using mean-field limits, and show that the model remains identifiable under specific information-bandwidth constraints. Finally, by incorporating rational inattention, they prove that limiting an agent's informational capacity is mathematically identical to a quantal-response equilibrium guided by an internal prior, deriving a sharp threshold where an agent shifts from ignoring information to paying attention.