The balance between adaptation to catalysts and competition radius shapes the total wealth, time variability and inequality

Abstract

The globalization of modern markets has led to the emergence of competition between producers in ever growing distances. This opens the interesting question in population dynamics of the effect of long-range competition. We here study a model of non-local competition to test the effect of the competition radius on the wealth distribution, using the framework of a stochastic birth-death process, with non-local interactions. We show that this model leads to non-trivial dynamics that can have implications in other domains of physics. Competition is studied in the context of the catalyst induced growth of autocatalytic agents, representing the growth of capital in the presence of investment opportunities. These agents are competing with all other agents in a given radius on growth possibilities. We show that a large scale competition leads to an extreme localization of the agents, where typically a single aggregate of agents can survive within a given competition radius. The survival of these aggregates is determined by the diffusion rates of the agents and the catalysts. For high and low agent diffusion rates, the agent population is always annihilated, while for intermediate diffusion rates, a finite agent population persists. Increasing the catalyst diffusion rate always leads to a decrease in the average agent population density. The extreme localization of the agents leads to the emergence of intermittent fluctuations, when a large aggregate of agents disappear. As the competition radius increases, so does the average agent density and its spatial variance as well as the volatility.