Distribution of wealth in a network model of the economy

We show, analytically and numerically, that wealth distribution in the Bouchaud–Mézard network model of the economy is described by a three-parameter generalized inverse gamma distribution. In the mean-field limit of a network with any two agents linked, it reduces to the inverse gamma distribution.

► We study a partially connected Bouchaud–Mézard network model.
► We formulate effective field theory of a partially connected network.
► In the stationary limit, wealth distribution is described by generalized inverse gamma function.
► In the mean field limit, generalized inverse gamma distribution reduces to inverse gamma distribution.
► Effective field theory describes a (random) small world network better than it describes the regular network.