A new probabilistic analysis of the yard-sale model

TL;DR

This paper provides a concise proof that wealth condensation almost surely occurs in Chakraborti's yard-sale model, and extends the analysis to a modified model with wealth advantage, highlighting the inevitability of wealth concentration.

Contribution

It offers a shorter proof of wealth condensation in the yard-sale model and extends the analysis to include a wealth-acquired advantage scenario.

Findings

Wealth condensation occurs almost surely in the original model.

The proof is significantly shorter than previous proofs.

The model extends to include a wealth advantage, still leading to wealth concentration.

Abstract

In Chakraborti's yard-sale model of an economy, identical agents engage in trades that result in wealth exchanges, but conserve the combined wealth of all agents and each agent's expected wealth. In this model, wealth condensation, that is, convergence to a state in which one agent owns everything and the others own nothing, occurs almost surely. We give a proof of this fact that is much shorter than existing ones and extends to a modified model in which there is a wealth-acquired advantage, i.e., the wealthier of two trading partners is more likely to benefit from the trade.