Mean field game problem for the optimal control of neuronal spiking activity

TL;DR

This paper models neuronal spiking activity using mean field game theory, deriving equilibrium strategies and approximations for large neuronal populations to understand collective neural dynamics.

Contribution

It introduces a novel mean field game framework for neuronal control, characterizing equilibria and approximating finite-player interactions in neural systems.

Findings

Characterized mean field equilibrium through fixed point analysis

Constructed approximate Nash equilibria for large neuron populations

Provided a mathematical framework linking individual control to collective neural behavior

Abstract

We study the mean field game problem for a nervous system consisting of a large number of neurons with mean-field interaction. In this system, each neuron can modulate its spiking activity by controlling its membrane potential to synchronize with others, thereby giving rise to a finite-player game problem. To address this, we first examine the corresponding mean field game problem and characterize the mean field equilibrium by solving a fixed point problem. Subsequently, leveraging the obtained mean field equilibrium, we construct an approximate Nash equilibrium for the finite-player game as the number of neurons is large.