  Most real life systems have a random component: the multitude of endogenous
and exogenous factors influencing them result in stochastic fluctuations of the
parameters determining their dynamics. These empirical systems are in many
cases subject to noise of multiplicative nature. The special properties of
multiplicative noise as opposed to additive noise have been noticed for a long
while. Even though apparently and formally the difference between free additive
vs. multiplicative random walks consists in just a move from normal to
log-normal distributions, in practice the implications are much more far
reaching. While in an additive context the emergence and survival of
cooperation requires special conditions (especially some level of reward,
punishment, reciprocity), we find that in the multiplicative random context the
emergence of cooperation is much more natural and effective. We study the
various implications of this observation and its applications in various
contexts.
