Diffusion-Induced Stabilization of Nonreciprocal Wealth Dynamics

Abstract

We study the stability of equal wealth shares in a spatial model combining local sharing, global redistribution, and random nonreciprocal interactions. On a two-dimensional square lattice in the infinite-system limit, the effect of local sharing depends on whether the influence of one site on another tends to have the same or opposite sign as the reverse influence. When these influences are nonnegatively correlated, diffusion reduces the redistribution required for stability, but a positive rate remains necessary. Negative correlations instead allow stability without redistribution, with the largest stability margin at finite diffusion and a return toward marginal stability at strong diffusion. This nonmonotonicity reflects a competition between spatial smoothing and the weakening of the stabilizing contribution of reciprocal anticorrelations. Equal shares can even remain stable under wealth-concentrating transfers, but only within an intermediate range of diffusion strengths.