Wealth Networks with Sharing Earnings and Expanding Trade Volume

Abstract

To explain the distribution of wealth in a society, we propose a growing network model in which each new node, representing an individual, becomes linked to other nodes. The links in the network represent contracts, which give both nodes chances to increase their wealth by producing earnings in proportion to the weight of the link, which represents a capacity for production. The two nodes connected by a link share these earnings in a given ratio and have chances to increase the weight of their link. The nodes have intrinsic levels of ability, allocated with a Beta distribution. We analyze the physical and the weighted degrees of the nodes, as well as the income and the wealth of the resulting networks. We show that, in all reasonable situations, these distributions stabilize, exhibiting scale-free tails. We also consider two societies with different ability distributions, while varying two key parameters, the sharing ratio and the rate at which the link weights are increased. As these parameters approach 1, the range scales expand, and the class of rich individuals becomes larger, and the poor and middle classes shrink. Finally, we show that the productivity of a network is optimized when the model is fair, meaning that each local contract is symmetric and the global ability distribution is uniform.