Invisible hand and arbitrage equilibrium in the self-organizing dynamics of pattern formation in ecological systems

TL;DR

This paper introduces a novel framework combining economics and game theory to explain pattern formation in ecological systems, demonstrating that self-interested behavior among mussels leads to spontaneous, stable collective patterns akin to an invisible hand.

Contribution

It presents a new theoretical approach called statistical teleodynamics to model self-organization in ecological systems driven by individual survival instincts.

Findings

Self-interested mussels lead to stable pattern formation.

Arbitrage equilibrium explains mussel bed patterns.

Analytical and computational validation of the model.

Abstract

Patterns in ecological systems such as mussel beds have been of considerable interest for a long time. Several physicochemical mechanisms have been proposed for their formation. Here, we propose a novel framework based on economics and game theory. Since mussels are biological agents instinctively driven by the survival purpose, we mathematically model this purpose explicitly using a new theoretical framework called statistical teleodynamics. We show both analytically and computationally that when every mussel pursues its own self-interest to survive, a stable collective order emerges spontaneously via self-organization. Thus, our mechanism is essentially the same as Adam Smith's invisible hand in a biological context. Our analysis reveals a new insight that the mussel bed patterns could be the result of arbitrage equilibrium in the competition for survival among the mussels.