  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.
