  Cooperation in repeated public goods game is hardly achieved, unless
contingent behavior is present. Surely, if mechanisms promoting positive
assortment between cooperators are present, then cooperators may beat
defectors, because cooperators would collect greater payoffs. In the context of
evolutionary game theory, individuals that always cooperate cannot win the
competition against defectors in well-mixed populations. Here, we study the
evolution of a population where fitness is obtained in repeated public goods
games and players have a fixed probability of playing the next round. As a
result, the group size decreases during the game. The population is well-mixed
and there are only two available strategies: always cooperate (ALLC) or always
defect (ALLD). Through numerical calculation and analytical approximations we
show that cooperation can emerge if the players stay playing the game, but not
for too long. The essential mechanism is the interaction between the transition
from strong to weak altruism, as the group size decreases, and the existence of
an upper limit to the number of rounds representing limited time availability.
