Paper: arXiv 2406.10978

Authors: Christoph Börgers, Claude Greengard

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.

Complexity vs Empirical Score

  • Math Complexity: 6.5/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a clear and elegant mathematical proof generalizing local wealth condensation in yard-sale network models without relying on martingale convergence. While mathematically sound and well-written, it is purely theoretical and completely lacks empirical backtesting or real-world financial data validation.

Research Flowchart

  flowchart TD
    A["Research Goal: Prove local wealth condensation in non-martingale Yard-Sale models"] --> B["Input: Agent Graph Network & Wealth-Dependent Biases"]
    B --> C["Model: Pairwise Trade Rules with Wealth/Poverty Advantages"]
    C --> D["Methodology: Develop Elementary Analytic Proof (Replacing Martingale Theorem)"]
    D --> E["Outcome 1: Validated Local Wealth Condensation (Impoverished Trading Partners)"]
    D --> F["Outcome 2: Proof Extended to Models with Wealth-Acquired & Poverty-Acquired Advantages"]