Application of the Fermi function in money exchange

TL;DR

This paper introduces a model for money exchange using the Fermi function, revealing phase transitions between stable and unstable wealth distributions across social graphs.

Contribution

It presents a novel application of the Fermi function in modeling economic exchanges and identifies conditions for phase transitions in wealth stability.

Findings

Fermi function effectively models buyer and seller behavior.

Phase transition equation between stable and unstable wealth states.

Conditions for wealth distribution stability across social graphs.

Abstract

In a money exchange process involving a seller and a buyer, we develop a straightforward model encompassing conservative, non-conservative, and systems with or without debt. Our model integrates the Fermi function to capture the behavior of buyers and sellers. Under certain circumstances, we identify an equation that marks the phase transition between a stable equal wealth state across all connected social graphs and an unstable equal wealth state in some connected social graph.