The norm game: punishing enemies and not friends

Three mean field models of the norm game are explored analytically. The strategies are: to obey the norm or not and to punish those who break it or not. The punishment, the temptation, the anger and the punishment cost are modeled by four parameters; for the fixed points, only two ratios of these parameters are relevant. For each model, we consider its variant with two mutually punishing groups. We show that all solutions are the same as for the case in one group. This means in particular, that in both groups the amount of defectors is the same.