International Journal of Modern Physics C Vol. 17, No. 3 (2006) 403–408 c  World Scientific Publishing Company SOCIAL HIERARCHIES WITH AN ATTRACTIVE SITE DISTRIBUTION G. G. NAUMIS * , M. DEL CASTILLO-MUSSOT, L. A. P ´ EREZ and G. J. V ´ AZQUEZ Instituto de F´ ısica, Universidad Nacional Aut´onoma de M´ exico Apartado Postal 20-364, 01000, M´ exico D. F., Mexico * naumis@fisica.unam.mx We reinvestigate the model of Bonabeau et al. 1 of self-organizing social hierarchies by including a distribution of attractive sites. Agents move randomly except in the case where an attractive site is located in its neighborhood. We find that the transition between an egalitarian society at low population density and a hierarchical one at high population density strongly depends on the distribution and percolation of the valuable sites. We also show how agent diffusivity is closely related to social hierarchy. Keywords : Social and economic systems; hierarchies; randomness; diffusivity. 1. Introduction An example of how hierarchical inequalities are created is given by the model of Bonabeau et al. 1 For example, the transition thousands of years ago from more egalitarian hunting and gathering societies to more hierarchical agricultural and city life could be described by a phase transition. 2 In the original Bonabeau model, agents diffuse on the square lattice to the four nearest neighbors. Agents (animals, individuals, communities, countries, etc) are initially equal and then they diffuse randomly. 1 When an agent moves onto an occupied site, a fight breaks out between the two and a memory function of the outcome is stored. The basic feature of the model is the introduction of an agent fitness based in its memory that evolves with the following rule. Whenever an agent wins, its probability to win again increases and when it loses, its probability to win again decreases. In the same spirit of the above model, there are some previous works. 3– 8 The phase transition between an egalitarian and hierarchical regime (or society) ob- served at a critical density was very weak 1 and it was reinforced 5,6 by introducing a feedback mechanism on the probability of an agent’s rise or fall in the hierarchy. Since these models produced the same number of weak (low fitness) and powerful (high fitness) agents in the hierarchy, a slight modification was made to reproduce the more realistic case of more weak agents. 8 Numerical simulations have been re- ported on the Bonabeau model on a fully connected graph, where a “forgetting” control parameter is crucial and spatial degrees of freedom are absent. 9 Later on, 403