Wealth networks with local redistribution

We propose a growing network model of the distribution of wealth in a society with local redistribution. Individuals, represented by nodes in the model, provide goods and services to one of their neighbors and they simultaneously produce wealth using goods and services received from their neighbors. A proportion of the wealth produced by a node is redistributed to its neighbors as a reward for the received goods and services. Nodes have different ability to produce wealth. We analyze the interaction between the wealth accumulation process and the structure of the network, and analyze also how the interaction is affected by the redistribution of wealth. It is investigated how rich nodes attract the individuals entering the network in this model. Under a reasonable distribution of ability, simulation result shows that the distribution of degree, i.e. number of neighbors of a node, is scale-free, and that the wealth distribution for the middle class is a log-normal distribution, while for the richest it shows a power-law behavior. We also show that the local redistribution of wealth has a significant effect on the distribution of both degree and wealth.