  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 class of agents. The fundamental
particularity of our model is that only a pairwise interaction between agents
of the opposite class is allowed. Agent fitness can thus only change by
competition among the two classes, 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 class 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 class. 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 class. Finally, a couple of 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.
