Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel
A kinetic exchange model is developed to investigate wealth distribution in a market. The model incorporates a value function that captures the agents’ psychological traits, governing their wealth allocation based on behavioral responses to perceived potential losses and returns. To account for the...
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MDPI AG
2025-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/27/1/64 |
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| author | Daixin Wang Shaoyong Lai |
| author_facet | Daixin Wang Shaoyong Lai |
| author_sort | Daixin Wang |
| collection | DOAJ |
| description | A kinetic exchange model is developed to investigate wealth distribution in a market. The model incorporates a value function that captures the agents’ psychological traits, governing their wealth allocation based on behavioral responses to perceived potential losses and returns. To account for the impact of transaction frequency on wealth dynamics, a non-Maxwellian collision kernel is introduced. Applying quasi-invariant limits and Boltzmann-type equations, a Fokker–Planck equation is derived. We obtain an entropy explicit stationary solution that exhibits exponential convergence to a lognormal wealth distribution. Numerical experiments support the theoretical insights and highlight the model’s significance in understanding wealth distribution. |
| format | Article |
| id | doaj-art-c2a18e0f99064b1095dec88dd4889dc8 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-c2a18e0f99064b1095dec88dd4889dc82025-01-24T13:31:52ZengMDPI AGEntropy1099-43002025-01-012716410.3390/e27010064Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision KernelDaixin Wang0Shaoyong Lai1School of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaSchool of Mathematics, Southwestern University of Finance and Economics, Chengdu 611130, ChinaA kinetic exchange model is developed to investigate wealth distribution in a market. The model incorporates a value function that captures the agents’ psychological traits, governing their wealth allocation based on behavioral responses to perceived potential losses and returns. To account for the impact of transaction frequency on wealth dynamics, a non-Maxwellian collision kernel is introduced. Applying quasi-invariant limits and Boltzmann-type equations, a Fokker–Planck equation is derived. We obtain an entropy explicit stationary solution that exhibits exponential convergence to a lognormal wealth distribution. Numerical experiments support the theoretical insights and highlight the model’s significance in understanding wealth distribution.https://www.mdpi.com/1099-4300/27/1/64wealth distributionvalue functionnon-Maxwellian collision kernelBoltzmann equation |
| spellingShingle | Daixin Wang Shaoyong Lai Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel Entropy wealth distribution value function non-Maxwellian collision kernel Boltzmann equation |
| title | Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel |
| title_full | Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel |
| title_fullStr | Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel |
| title_full_unstemmed | Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel |
| title_short | Wealth Distribution Involving Psychological Traits and Non-Maxwellian Collision Kernel |
| title_sort | wealth distribution involving psychological traits and non maxwellian collision kernel |
| topic | wealth distribution value function non-Maxwellian collision kernel Boltzmann equation |
| url | https://www.mdpi.com/1099-4300/27/1/64 |
| work_keys_str_mv | AT daixinwang wealthdistributioninvolvingpsychologicaltraitsandnonmaxwelliancollisionkernel AT shaoyonglai wealthdistributioninvolvingpsychologicaltraitsandnonmaxwelliancollisionkernel |