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SOE: Fachverband Physik sozio-ökonomischer Systeme

SOE 25: Economic Networks

SOE 25.1: Talk

Friday, March 22, 2024, 11:00–11:15, MA 001

Rethinking the Lotka-Volterra equations as a model of inequality — •Fabian Aguirre Lopez — Ecole Polytechnique, Paris, France

We recast the Lotka-Volterra model as an effective model for the interaction between the wealth of agents in an economy. The model is chosen to have a single parameter that controls whether agents are competing or cooperating. And, most importantly, the agents interact through a random network with a prescribed degree distribution.

In the competitive case, the effect of the network of interactions is negative. For some agents this only means relaxing to a small value, but interestingly, for some agents with high degree it implies that they go extinct. We can calculate exactly both the critical degree for extinction and the fraction of survivors. In the cooperative case, there is no extinction, but interestingly there is a regime where the global wealth diverges. It is determined by the network structure and we refer to it as the "wealth creation regime". Amazingly, we find that in this new scaling we have relative extinctions in the system, but now for the low degrees. The meaning of these extinctions is that low enough degree nodes have a vanishing fraction of the total wealth. We can also calculate exactly both the critical degree and the fraction of survivors.

We have shown that in this minimal model, wealth creation goes hand in hand with increasing inequality, as nodes with higher number of interactions will benefit more and more as the total wealth diverges. This phenomenon is strongly dependent on the network structure as all of these results trivialize if the graph has no degree heterogeneity.

Keywords: networks; inequality; mean-field; dynamics; group behavior