  Norms, defined as generally accepted behaviour in societies without central
authority (and thus distinguished from laws), are very powerful mechanism
leading to coherent behaviour of the society members. This paper examines,
within a simple numerical simulation, the various effects that may lead to norm
formation and stability. The approach has been first used by Axelrod, who
proposed two step model of norm and meta-norm enforcement. We present here an
extension and detailed analysis of the original work, as well as several new
ideas that may bear on the norm establishment mechanisms in societies. It turns
out that a relatively simple model for simulated norm enforcement predicts
persistent norm breaking even when it is associated with high punishment
levels. The key factors appear to be the combination of the level of penalty
for breaking the norm and proximity of norm enforcers. We also study a totally
different mechanism of norm establishment, without meta-norms but using instead
the direct bonus mechanism to norm-enforcers.
