  Spatial structure is known to have an impact on the evolution of cooperation,
and so it has been intensively studied during recent years. Previous work has
shown the relevance of some features, such as the synchronicity of the
updating, the clustering of the network or the influence of the update rule.
This has been done, however, for concrete settings with particular games,
networks and update rules, with the consequence that some contradictions have
arisen and a general understanding of these topics is missing in the broader
context of the space of 2x2 games. To address this issue, we have performed a
systematic and exhaustive simulation in the different degrees of freedom of the
problem. In some cases, we generalize previous knowledge to the broader context
of our study and explain the apparent contradictions. In other cases, however,
our conclusions refute what seems to be established opinions in the field, as
for example the robustness of the effect of spatial structure against changes
in the update rule, or offer new insights into the subject, e.g. the relation
between the intensity of selection and the asymmetry between the effects on
games with mixed equilibria.
