  The public goods game is a model of a society investing some assets and
regaining a profit, although can also model biological populations. In the
classic public goods game only two strategies compete: either cooperate or
defect; a third strategy is often implemented to asses punishment, which is a
mechanism to promote cooperation. The conditions of the game can be of a
dynamical nature, therefore we study time-dependent effects such an as
oscillation in the enhancement factor, which accounts for productivity changes
over time. Furthermore, we continue to study time dependencies on the game with
a delay on the punishment time. We conclude that both the oscillations on the
productivity and the punishment delay concur in the detriment of cooperation.
