  We discuss the simulations of the norm game between players at nodes of a
directed random network. The final boldness of the players can vary with the
initial one as the $\Theta$ function. One of the conditions of this behaviour
is that the player who does not punish automatically becomes a defector. The
threshold value of the initial boldness can be interpreted as a norm strength.
It increases with the punishment and decreases with its cost. Surprisingly, it
also decreases with the number of potential punishers. The numerical results
are discussed in the context of the statistical data on crimes in Northern
Ireland and New Zealand, on divorces in USA, and on the alcohol consumption in
Poland.
