Wealth Distribution Under Power Trading Frequencies and Transitions of Agents

We construct a kinetic model to investigate transactions among two populations from different countries. In our model, power collision kernels and a transfer operator are introduced into the Boltzmann equation. Through the method of continuous trading limits, we derive the Fokker-Planck equations and find their entropy steady-state solutions for two special cases. Numerical experiments are provided to illustrate our results under different parameters. The conclusion shows that the increase of agents' trading willingness and the decrease of agents' transaction rate (the increase of saving rate) narrow the gap in agents' wealth. If there is a significant disparity in the trading willingness between agents from the two countries, the overall wealth distribution exhibits a bimodal distribution pattern.