Self-organization of extreme inequalities in a competitive society

Abstract

On the basis of a random walk model, we investigate the self-organization of inequality in a model competitive society which consists of two kinds of individuals; one is warlike-challenging individuals who always try to ght and ght with the wealthiest or strongest neighbor, and the other is pacic-timid individuals who always try not to ght and when necessary ght with the poorest or weakest neighbor. When two individuals meet on a lattice site, they ght and the winner deprives a unit wealth from the loser keeping its position, where the winning odd is determined by a sigmoid function of the dierence in their wealths. At the same time, the wealth or debt of individuals relaxes to zero at a constant rate when the wealth or debt is large. Using Monte Carlo simulation we determine states of social inequality in the entire parameter space spanned by the population density and the fraction of pacic-timid individuals in the population on the basis of the prole of the wealth distribution plotted against the ranking. We nd an egalitarian state, and one normal inequal and three dierent extreme inequal states, the plutonomy, the gap inequality and the terrace inequality. In order to elucidate the origin of the self-organization, we investigate a model society consisting of individuals who have dierent moving strategies and no specic ghting strategy. It is concluded that the extreme inequalities are the consequence of the coexistence of dierent ghting strategies.