  We explore the evolutionary dynamics of two games - the Prisoner's Dilemma
and the Snowdrift Game - played within distinct networks (layers) of
interdependent networks. In these networks imitation and interaction between
individuals of opposite layers is established through interlinks. We explore an
update rule in which revision of strategies is a biased imitation process:
individuals imitate neighbors from the same layer with probability p, and
neighbors from the second layer with complementary probability 1 - p. We
demonstrate that a small decrease of p from p = 1 (which corresponds to
forbidding strategy transfer between layers) is sufficient to promote
cooperation in the Prisoner's Dilemma subpopulation. This, on the other hand,
is detrimental for cooperation in the Snowdrift Game subpopulation. We provide
results of extensive computer simulations for the case in which layers are
modelled as regular random networks, and support this study with analytical
results for coupled well-mixed populations.
