Bio-Inspired Dynamic Collective Choice in Large-Population Systems: A Robust Mean-Field Game Perspective

Area of Science:

• Complex Systems
• Game Theory
• Control Theory
• Collective Behavior

Background:

• Biological systems, like honeybee swarms, exhibit sophisticated collective decision-making.
• Large-scale systems with heterogeneous agents face complexity due to individual differences and external disturbances.
• Existing models often struggle to capture emergent behaviors in dynamic, large-population scenarios.

Purpose of the Study:

• To model and analyze dynamic collective choice problems in large, heterogeneous agent systems.
• To replicate advantageous collective decision-making features observed in biological systems.
• To develop robust control strategies that ensure agents converge to a common goal while maintaining group cohesion.

Main Methods:

• Formulation as a robust mean-field game with non-convex and non-smooth cost functions.
• Application of the Nash equivalence principle to simplify the problem.
• Design of optimal control strategies and worst-case disturbance identification.
• Establishment of a mean-field system for population behavior estimation.

Main Results:

• Development of population-size-independent optimal control strategies and disturbance analysis.
• Demonstration that the designed strategies achieve an ϵ_N-Nash equilibrium, approaching perfect equilibrium as population size increases.
• Validation of the approach through two simulation examples showcasing emergent collective decision-making.

Conclusions:

• The proposed robust mean-field game framework effectively models and solves complex collective decision-making problems.
• The developed strategies enable large, heterogeneous systems to exhibit emergent, biologically inspired collective behaviors.
• The findings offer a theoretical foundation for designing decentralized control systems with robust emergent properties.