More Opportunities than Wealth: A Network of Power and Frustration

Abstract: We introduce a minimal agent-based model to qualitatively conceptualize the allocation of limited wealth among more abundant opportunities. We study the interplay of power, satisfaction and frustration in distribution, concentration, and inequality of wealth. Our framework allows us to compare subjective measures of frustration and satisfaction to collective measures of fairness in wealth distribution, such as the Lorenz curve and the Gini index. We find that a completely libertarian, law-of-the-jungle setting, where every agent can acquire wealth from, or lose wealth to, anybody else invariably leads to a complete polarization of the distribution of wealth vs. opportunity. The picture is however dramatically modified when hard constraints are imposed over agents, and they are limited to share wealth with neighbors on a network. We then propose an out of equilibrium dynamics {\it of} the networks, based on a competition between power and frustration in the decision-making of agents that leads to network coevolution. We show that the ratio of power and frustration controls different dynamical regimes separated by kinetic transitions and characterized by drastically different values of the indices of equality. The interplay of power and frustration leads to the emergence of three self-organized social classes, lower, middle, and upper class, whose interactions drive a cyclical regime.