Population and Asset Distributions in Economically Competitive Activities: a Rate-Equation Approach

We introduce a simple asset migration model for the wealth redistribution in economical activities, in which a unit of asset migrates from one individual to another whenever they interact. By means of the mean-field rate equation, we have analysed the dynamic behaviour of the system. In the random migration case, the asset distribution of individuals takes the standard Gaussian form and consistently decreases to zero at the end. As for the system in which only the richer can gain assets from the poorer, it is found that the individual asset distribution is discontinuous at a critical point and only the individuals with asset absolute value less than a cutoff value have a uniform and non-zero distribution. Moreover, the result shows that for the system with migration bias the assets of the individuals may have a cutoff value at each given time, which is different from the system without migration bias.