Self organization of social hierarchy in competitive societies

Abstract

The aim of this paper is to understand the condition of emergence of social hierarchy in a competitive society. We introduce a minimal model which incorporates cost for participating in fighting in order to understand effects of the difference between the gain for a winner and the loss for a loser. We show numerically and analytically that phase transition from an egalitarian state to hierarchical states occurs in two steps as the frequency of fighting is increased for any value of cost except when the reward is equal to the cost or to twice of the cost, and when no cost is required. Furthermore, we determine the phase diagram consisting of one egalitarian phase and three distinct hierarchical phases in the parameter space of the cost and the frequency of fighting. © 2011 The Physical Society of Japan.