There are two types of extreme form of hierarchy, one is the plutonomy where small fraction of winners and losers and many people in the middle class appear and the other a divided hierarchy where half of population become winners and the remaining half become losers. It is an important question to find out what traits of competitive society lead to the extreme form of hierarchy.

I first investigate conditions for emergence of plutonomy in a model society where individuals participate in a competition with equal right and the winner deprives wealth from the loser. I show that the plutonomy can be self-organized when individuals grouped into several classes compete with those in the same class for a certain period (season) and they are regrouped at the end of every season.

Next, I study a model society consisting of bellicose individuals who always try to fight and fight with the strongest neighbor. In this society, individuals make random walk on a square lattice, and when two individuals encounter they fight each other and the winner deprives wealth from the loser. I show that the order of move plays an important role and the plutonomy emerges when individuals have the same right to move first.

Finally, I discuss the self-organization of hierarchy in a model society which consists of the bellicose individuals and pacific individuals who always try not to fight and when necessary fight with the weakest neighbor. I show that there are two transitions when the population density is increased; one is a transition from the egalitarian society to a hierarchical society I where winners, losers and middle classes coexist and the other is a transition from the hierarchical society I to a hierarchical society II where winners and losers exist but no middle classes exist, that is the divided hierarchy. We also show that clusters consisting mostly of bellicose individuals appear in the hierarchical society I.

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1. Self-organization of extreme inequalities