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<p>We study the redistributive effects of delayed retirement using a novel nonlinear kinetic-mean-field game framework. This model couples a Fokker-Planck equation for wealth dynamics with a Hamilton-Jacobi-Bellman equation for individual optimization, incorporating three redistribution mechanisms: uniform, inverse-proportional, and exponential. Numerical simulations are conducted on a fully specified kinetic-mean-field game system, employing positivity preserving fluxes and backward forward solvers with grid refinement studies to certify convergence. Our results reveal that exponential redistribution schemes are most effective in reducing inequality by concentrating wealth in the middle income range, while inverse-proportional schemes enhance participation among lower-wealth individuals. In contrast, uniform redistribution yields stable but homogeneous outcomes, with low sensitivity to individual strategic adjustments. This work is the first to quantitatively assess the impact of delayed retirement policies through the lens of mean-field game theory, providing valuable insights into designing redistribution policies that balance equity, efficiency, and incentive compatibility.</p>

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Wealth Redistribution and Strategic Behavior under Delayed Retirement: A Fokker–Planck and Mean-Field Game Approach

  • 期刊论文

  • 发表日期：

    2026年3月17日

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  • Yuhui Jin,
  • Chong Lai

摘要

We study the redistributive effects of delayed retirement using a novel nonlinear kinetic-mean-field game framework. This model couples a Fokker-Planck equation for wealth dynamics with a Hamilton-Jacobi-Bellman equation for individual optimization, incorporating three redistribution mechanisms: uniform, inverse-proportional, and exponential. Numerical simulations are conducted on a fully specified kinetic-mean-field game system, employing positivity preserving fluxes and backward forward solvers with grid refinement studies to certify convergence. Our results reveal that exponential redistribution schemes are most effective in reducing inequality by concentrating wealth in the middle income range, while inverse-proportional schemes enhance participation among lower-wealth individuals. In contrast, uniform redistribution yields stable but homogeneous outcomes, with low sensitivity to individual strategic adjustments. This work is the first to quantitatively assess the impact of delayed retirement policies through the lens of mean-field game theory, providing valuable insights into designing redistribution policies that balance equity, efficiency, and incentive compatibility.