Directed Random Markets: Connectivity determines Money

TL;DR

This paper explores how network topology influences money distribution in economic models, showing that directed exchanges cause the mean money per agent to depend linearly on node degree, unlike undirected cases.

Contribution

It introduces a new class of directed exchange models on networks, demonstrating the impact of topology on money distribution and establishing a linear relation between money and node degree.

Findings

Undirected exchange models produce gamma-like distributions unaffected by network topology.

Directed exchanges cause the mean money per agent to depend linearly on node degree.

Topology becomes a crucial factor in money distribution under directed exchange rules.

Abstract

Boltzmann-Gibbs distribution arises as the statistical equilibrium probability distribution of money among the agents of a closed economic system where random and undirected exchanges are allowed. When considering a model with uniform savings in the exchanges, the final distribution is close to the gamma family. In this work, we implement these exchange rules on networks and we find that these stationary probability distributions are robust and they are not affected by the topology of the underlying network. We introduce a new family of interactions: random but directed ones. In this case, it is found the topology to be determinant and the mean money per economic agent is related to the degree of the node representing the agent in the network. The relation between the mean money per economic agent and its degree is shown to be linear.