We investigate the self-organization of inequality in a model society which consists of warlike-challenging (WC) individuals who always try to fight and fight with the strongest neighbor, and pacific-timid (PT) individuals who always try not to fight and when necessary fight with the weakest neighbor. The population density is controlled by changing the lattice size on which each individual makes a random walk. When two individuals meet on a lattice site, they fight 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 difference in their wealths. The wealth of individuals relaxes to zero when they do not participate in fighting. Using Monte Carlo simulation, we analyze the structure of social inequality in the entire parameter space spanned by the population density and the fraction of pacific-timid individuals in the population. We determine the phases in the entire parameter space on the basis of an order parameter defined by the fluctuation in winning probabilities and the profile of the wealth distribution. We find an egalitarian phase, and one normal inequal and three different extreme inequal phases which are the plutonomy, the gap inequality and the terrace inequality. It is concluded that the extreme inequalities are the consequence of the coexistence of different fighting strategies.