  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.
