Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel

Area of Science:

• Economic modeling
• Statistical physics
• Behavioral economics

Background:

• Understanding wealth distribution is crucial for economic stability.
• Existing models often simplify agent behavior and market dynamics.
• Psychological factors significantly influence economic decision-making.

Purpose of the Study:

• To develop a kinetic exchange model for wealth distribution.
• To incorporate agent psychological traits and transaction frequency.
• To analyze the resulting wealth distribution patterns.

Main Methods:

• Developed a kinetic exchange model with a value function.
• Introduced a non-Maxwellian collision kernel for transaction frequency.
• Derived a Fokker-Planck equation using quasi-invariant limits and Boltzmann-type equations.

Main Results:

• Obtained an entropy explicit stationary solution.
• Demonstrated exponential convergence to a lognormal wealth distribution.
• Numerical experiments validated the theoretical findings.

Conclusions:

• The developed model provides a robust framework for understanding wealth distribution.
• Agent psychology and transaction frequency are key drivers of lognormal distribution.
• The model offers significant insights into market dynamics and economic behavior.