Arbitrage Equilibrium, Invariance, and the Emergence of Spontaneous Order in the Dynamics of Bird-like Agents

The physics of active biological matter, such as bacterial colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Current theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these approaches do not seem to recognize explicitly their critical feature: namely, the role of survival-driven purpose and the attendant pursuit of maximum utility. Here, we propose a game-theoretic framework, statistical teleodynamics, that demonstrates that the bird-like agents self-organize dynamically into flocks to approach a stable arbitrage equilibriumof equal effective utilities. This is essentially the invisible handmechanism of Adam Smith's in an ecological context. What we demonstrate is for ideal systems, similar to the ideal gas or Ising model in thermodynamics. The next steps would involve examining and learning how real swarms behave compared to their ideal versions. Our theory is not limited to just birds flocking but can be adapted for the self-organizing dynamics of other active matter systems.