Wealth distribution in a closed system of wealth-limited interaction

Abstract

We model a closed economic system with interactions that generate the features of empirical wealth distribution across all wealth brackets, namely an exponential or Gibbsian trend in the lower wealth range and a power law or Pareto trend in the higher range. We show that the wealth distribution is Pareto if the interaction is restricted to pairs of agents with nearly the same wealth and is Gibbsian if the interaction is unrestricted. We introduce a parameter β to define the interaction range. For a non-mutual choice, where the richer agent unilaterally chooses a partner, the transition happens at β = 0.10 while for a mutual choice, where both agent must fall within each others' interaction range, the transition is at β = 0.60. We show how a mixed distribution is obtained when the choice of partner is either restricted or unrestricted depending on whether the agent's wealth is below a parameter wlimit. To match the simulated Pareto exponents to empirical results, we add a saving-propensity rule that restricts the amount an agent wagers in each transaction.