Nash Equilibrium-Driven Adaptive Behavior in Swarm Intelligence with Self-Organizing Maps

Abstract

This paper proposes a swarm intelligence model that employs classical boid
flocking dynamics combined with non-cooperative game-theoretic methods, specifically Nash Equilibrium, to simulate adaptive decision-making in multi-agent systems. The work leverages a payoff matrix based on fundamental flocking behaviors: cohesion, alignment, and separation, to enable each agent to dynamically optimize its own strategy based on local interactions within the group. The simulation introduces Self-Organizing Maps (SOMs) for clustering and behavior adaptation, providing a machine learning perspective on agent categorization and role differentiation. To simulate real-world unpredictability, stochastic noise is used to understand how varying noise levels influence collective alignment and coherence. The results demonstrate the impact of environmental factors on emergent swarm behavior and showcase the benefits of combining machine learning and game theory for adaptive control in distributed systems. This work provides valuable insights into the interplay between noise, decision-making, and flocking dynamics, with broader applications in robotics, swarm intelligence, and autonomous systems.