Arbitrage Equilibrium and the Invisible Hand in the Self-organizing Dynamics of Ants, Birds, and Peo

Venkat Venkatasubramanian, Columbia University
One might wonder what economic concepts like arbitrage and the invisible hand are doing in the dynamics of biological and ecological systems. As it turns out, plenty!
The physics of active matter, such as ant colonies and bird flocks, exhibiting interesting self-organizing dynamical behavior has gained considerable importance in recent years. Recent theoretical advances use techniques from hydrodynamics, kinetic theory, and non-equilibrium statistical physics. However, for biological agents, these don t seem to recognize explicitly their critical feature, namely, the role of survival-driven purpose and the attendant pursuit of maximum utility.
In this talk, I will present a novel game-theoretic framework, called statistical teleodynamics, that accounts for this feature explicitly and shows how it can be integrated with conventional statistical mechanics to develop a unified theory of arbitrage equilibrium in active matter.
The theory proposes a spectrum of self-actualizing capabilities, going from none to completely strategic decision-making, and envisions the various examples of active matter systems occupying someplace in this spectrum. I will show how statistical teleodynamics reduces to familiar results in statistical mechanics in the limit of zero self-actualization. At the other extreme, in an economic setting, it provides novel insights into the emergence of income distributions and their fairness in an ideal free-market society. As examples of agents in between these limits, I will discuss how the theory predicts pattern formation in mussel beds, the emergence of ant craters, and the flocking of birds.
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