What the Boltzmann money game teaches us about statistical mechanics (and maybe economics)

TL;DR

This paper explores how various stochastic models of wealth redistribution, including multi-agent and asymmetric transfer games, naturally lead to statistical mechanics distributions, revealing deep connections between economics and physics.

Contribution

It demonstrates that a broad class of fair and asymmetric money transfer models produce steady states described by canonical and microcanonical distributions, linking economic models to statistical mechanics.

Findings

Reversible money games lead to canonical distributions.

Multi-agent transfer models exhibit similar statistical properties.

Even non-reversible games can produce these distributions.

Abstract

This note explains why a large class of fair, or reversible "money games", i.e., stochastic models of wealth redistribution among agents, lead to steady states described by canonical and microcanonical distributions. The games considered include, for example, ones where more than two agents can be simultaneously involved in money transfers (similarly to many-body collisions in chemical kinetics) and where amounts transferred between agents are random. At the same time, money games that break time reversal symmetry can also lead to the canonical/microcanonical distributions, as illustrated by an explicit example.