Emergence of social hierarchies in a society with two competitive groups

Agent-based models describing social interactions among individuals can help to better understand emerging macroscopic patterns in societies. One of the topics which is worth tackling is the formation of different kinds of hierarchies that emerge in social spaces such as cities. Here we propose a Bonabeau-like model by adding a second group of agents. The fundamental particularity of our model is that only a pairwise interaction between agents of the opposite group is allowed. Agent fitness can thus only change by competition among the two groups, while the total fitness in the society remains constant. The main result is that for a broad range of values of the model parameters, the fitness of the agents of each group show a decay in time except for one or very few agents which capture almost all the fitness in the society. Numerical simulations also reveal a singular shift from egalitarian to hierarchical society for each group. This behaviour depends on the control parameter $\eta$, playing the role of the inverse of the temperature of the system. Results are invariant with regard to the system size, contingent solely on the quantity of agents within each group. Finally, scaling laws are provided thus showing a data collapse from different model parameters and they follow a shape which can be related to the presence of a phase transition in the model.