Paper: arXiv 2308.01485

Authors: Christoph Börgers, Claude Greengard

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.

Complexity vs Empirical Score

  • Math Complexity: 8.0/10
  • Empirical Rigor: 1.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a concise mathematical proof extending the yard-sale model to include wealth-acquired advantages using probability theory. While theoretically strong with high mathematical density, it completely lacks empirical validation or real-world market data analysis.

Research Flowchart

  flowchart TD
    A[Research Goal: Prove wealth condensation in Yard-Sale Model] --> B[Input: Chakraborti Yard-Sale Model & Wealth-Advantage Extension]
    B --> C[Methodology: Apply Probabilistic Analysis & Martingale Theory]
    C --> D[Model Trade Dynamics: Conserve total & expected wealth]
    D --> E[Compute Asymptotics: Evaluate long-term wealth distribution]
    E --> F[Outcome: Shortened proof of almost sure condensation to 1 agent]