  The sampling of interaction partners depends on often implicit modelling
assumptions, yet has marked effects on the dynamics in evolutionary games. One
particularly important aspect is whether or not competitors also interact.
Population structures naturally affect sampling such that in a microscopic
interpretation of the replicator dynamics in well-mixed populations competing
individuals do not interact but do interact in structured populations. In
social dilemmas interactions with competitors invariably inhibit cooperation
while limited local interactions in structured populations support cooperation
by reducing exploitation through cluster formation. These antagonistic effects
of population structures on cooperation affect interpretations and the
conclusions depend on the details of the comparison. For example, in the
Snowdrift game, spatial structure may inhibit cooperation when compared to the
replicator dynamics. However, modifying the replicator dynamics to include
interactions between competitors lowers the equilibrium frequency of
cooperators, which changes the conclusions and space is invariably beneficial,
just as in the Prisoner's Dilemma. These conclusions are confirmed by
comparisons with random matching models, which mimic population structures but
randomly reshuffle individuals to inhibit spatial correlations. Finally, the
differences in the dynamics with and without interactions among competing
individuals underlies the differences between death-birth and birth-death
updating in the spatial Moran process: death-birth supports cooperation because
competitors tend not to interact whereas they tend to do for birth-death
updating and hence cooperators provide direct support to competitors to their
own detriment.
