Discrimination emerging through spontaneous symmetry breaking in a spatial prisoner's dilemma model with multiple labels.

Social discrimination seems to be a persistent phenomenon in many cultures. It is important to understand the mechanisms that lead people to judge others by the group to which they belong rather than individual qualities. It was recently shown that evolutionary (imitation) dynamics can lead to a hierarchical discrimination between agents marked with observable, but otherwise meaningless, labels. These findings suggest that it can give useful insight to describe the phenomenon of social discrimination in terms of spontaneous symmetry breaking. The investigations so far have, however, only considered binary labels. In this contribution we extend the investigations to models with up to seven different labels. We find the features known from the binary label model remain remarkably robust when the number of labels is increased. We also discover a new feature, namely that it is more likely for neighbors to have strategies which are similar, in the sense that they agree on how to act toward a subset of the labels.