Discrimination in Heterogeneous Games

In this paper, we consider coordination and anti-coordination heterogeneous games played by a finite population formed by different types of individuals who fail to recognize their own type but do observe the type of their opponent. We show that there exists symmetric Nash equilibria in which players discriminate by acting differently according to the type of opponent that they face in anti-coordination games, while no such equilibrium exists in coordination games. Moreover, discrimination has a limit: the maximum number of groups where the treatment differs is three. We then discuss the theoretical results in light of the observed behavior of people in some specific psychological contexts.