Application of the Deffuant model in money exchange

Paper: arXiv 2307.02512

Authors: Hsin-Lun Li

Abstract

A money transfer involves a buyer and a seller. A buyer buys goods or services from a seller. The money the buyer decreases is the same as that the seller increases. At each time step, a pair of socially connected agents are selected and transact in agreed money. We evolve the Deffuant model to a money exchange system and study circumstances under which asymptotic stability holds, or equal wealth can be achieved.

Complexity vs Empirical Score

• Math Complexity: 5.5/10
• Empirical Rigor: 2.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper adapts the Deffuant opinion dynamics model to a agent-based money exchange system, offering theoretical derivations for asymptotic stability and wealth convergence. However, it lacks empirical validation against real-world transaction data or empirical backtests, leaving it primarily as a mathematical econophysics exercise.

Research Flowchart

  flowchart TD
    A["Research Goal: Conditions for Asymptotic Stability & Equal Wealth in Money Exchange"] --> B["System Input: Agent Network & Initial Wealth Distribution"]
    B --> C["Methodology: Evolve Deffuant Model for Pairwise Money Transactions"]
    C --> D["Simulation Process: Select Connected Agent Pair & Transact Agreed Amount at Step t"]
    D --> E["Outcome 1: Identify Circumstances Reaching Asymptotic Stability"]
    D --> F["Outcome 2: Identify Conditions for Equal Wealth Distribution"]