Local wealth condensation for yard-sale models with wealth-dependent biases

TL;DR

This paper provides a new, elementary proof for local wealth condensation in yard-sale models, extending the understanding to models with wealth- or poverty-based advantages, beyond the classical martingale approach.

Contribution

It introduces a simpler proof technique for wealth condensation that applies to models with wealth- or poverty-dependent biases, broadening theoretical insights.

Findings

Local wealth condensation occurs in yard-sale models with trading restrictions.

The new proof applies to models with wealth- or poverty-based advantages.

Results extend the classical martingale convergence theorem to more complex models.

Abstract

In Chakraborti's yard-sale model of an economy, identical agents engage in pairwise trades, resulting in wealth exchanges that conserve each agent's expected wealth. Doob's martingale convergence theorem immediately implies almost sure wealth condensation, i.e., convergence to a state in which a single agent owns the entire economy. If some pairs of agents are not allowed to trade with each other, the martingale convergence theorem still implies local wealth condensation, i.e., convergence to a state in which some agents are wealthy, while all their trading partners are impoverished. In this note, we propose a new, more elementary proof of this result. Unlike the proof based on the martingale convergence theorem, our argument applies to models with a wealth-acquired advantage, and even to certain models with a poverty-acquired advantage.