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Wealth distribution models with regulations: Dynamics and equilibria

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  • Cardoso, Ben-Hur Francisco
  • Gonçalves, Sebastián
  • Iglesias, José Roberto

Abstract

Simple agent based exchange models are a commonplace in the study of wealth distribution in an artificial economy. Generally, in a system that is composed of many agents characterized by their wealth and risk-aversion factor, two agents are selected sequentially and randomly to exchange wealth, allowing its redistribution. Here we analyze how the effect of social protection policies, which favor agents of lower wealth during the exchange, influences the stability and some relevant economic indicators of the system. On the other hand, we study how periods of interruption of these policies produce, in the short and long term, changes in the system. In all cases, a steady state is reached, but with varying relaxation times. We conclude that regulations may improve economic mobility and reduce inequality. Moreover, our results indicate that the removal of social protection entails a high cost associated with the hysteresis of the distribution of wealth. Economic inequalities increase during the period without social protection and decrease when they are restored. But recovery to the initial equilibrium may take longer than it took to disturb it. In some extreme cases, inequality is irreversible.

Suggested Citation

  • Cardoso, Ben-Hur Francisco & Gonçalves, Sebastián & Iglesias, José Roberto, 2020. "Wealth distribution models with regulations: Dynamics and equilibria," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    • Handle: RePEc:eee:phsmap:v:551:y:2020:i:c:s0378437120300406
    DOI: 10.1016/j.physa.2020.124201
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    2. Giordano, Lautaro & Cortés, Ignacio & Gonçalves, Sebastian & Laguna, María Fabiana, 2025. "Limiting risk to reduce inequality: Insights from the Yard-Sale model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 676(C).
    3. Dias, Thiago & Gonçalves, Sebastián, 2024. "Effectiveness of wealth-based vs exchange-based tax systems in reducing inequality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 641(C).
    4. Istvan Gere & Szabolcs Kelemen & Geza Toth & Tamas Biro & Zoltan Neda, 2021. "Wealth distribution in modern societies: collected data and a master equation approach," Papers 2104.04134, arXiv.org.
    5. Lin, Chuandong & Cui, Lijie, 2026. "Kinetic modeling of wealth distribution under individual and collective transactions with heterogeneous saving propensities," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 681(C).
    6. Lima, Hugo & Vieira, Allan R. & Anteneodo, Celia, 2022. "Nonlinear redistribution of wealth from a stochastic approach," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    7. Tiago Sousa Araújo Cassiano & Fábio Luís Oliveira Paula & Leonardo Luiz e Castro, 2024. "Does a severe regulatory policy on trade benefit the economy?," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(7), pages 1-10, July.
    8. Skare, Marinko & Gavurova, Beata & Blažević Burić, Sanja, 2024. "Artificial intelligence and wealth inequality: A comprehensive empirical exploration of socioeconomic implications," Technology in Society, Elsevier, vol. 79(C).
    9. Gere, István & Kelemen, Szabolcs & Tóth, Géza & Biró, Tamás S. & Néda, Zoltán, 2021. "Wealth distribution in modern societies: Collected data and a master equation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 581(C).
    10. Ilda Inácio & José Velhinho, 2022. "Comments on Mathematical Aspects of the Biró–Néda Model," Mathematics, MDPI, vol. 10(4), pages 1-10, February.
    11. Cui, Lijie & Lin, Chuandong, 2021. "A simple and efficient kinetic model for wealth distribution with saving propensity effect: Based on lattice gas automaton," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    12. Thomas Gottfried & Stefan Grosskinsky, 2025. "Wages and capital returns in a generalized Pólya urn," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 20(2), pages 477-518, April.
    13. Barros, Iago N. & Martins, Marcelo L., 2025. "Effects of taxes, redistribution actions and fiscal evasion on wealth inequality: An agent-based model approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 679(C).
    14. Kohlrausch, Gustavo L. & Gonçalves, Sebastian, 2024. "Wealth distribution on a dynamic complex network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 652(C).
    15. Neñer, Julian & Laguna, María Fabiana, 2021. "Optimal risk in wealth exchange models: Agent dynamics from a microscopic perspective," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    16. Francisco Cardoso, Ben-Hur & Gonçalves, Sebastián & Iglesias, José Roberto, 2023. "Why equal opportunities lead to maximum inequality? The wealth condensation paradox generally solved," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

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