2025/11/11 by Jiyuan Lyu, Jihyuan Liuh, Liuh, Jihyuan
Economics, Econometrics and Finance · #Complex Systems and Time Series Analysis #Economic and Technological Innovation #Economic theories and models #econ.GN #physics.soc-ph #q-fin.EC
paper · pdf · doi:10.48550/arxiv.2511.08202
openalex publication_date 2025/11/11 · openalex created_date 2025/11/13 · openalex updated_date 2026/07/28
The Boltzmann wealth model provided by the Mesa framework is a classic example in agent-based modeling, yet its statistical properties are typically analyzed only through numerical simulation. This paper studies a mean-field version of the model, replacing local interactions with global random matching and adopting a synchronous update scheme. By establishing a mean-field master equation for the wealth distribution and employing the probability generating function method, we obtain a closed-form expression for the steady-state generating function, and analytically determine the model parameters. We further derive the variance, Gini coefficient, and tail asymptotic behavior of the steady-state wealth distribution. Numerical simulations of the corresponding mean-field agent-based model agree well with the theoretical predictions. This paper provides an analytical benchmark for this mean-field model, which can serve as a reference for theoretical analysis and result validation in related agent-based simulations.