"Only when the population outgrows the game available would it have been necessary for humans to turn to farming."
This would seem to be a natural end to the process wouldn't it, and I personally wholeheartedly agree. However, some would say, with quite a strong argument I think, that man is always one to take the lazy option. The discovery/invention of farming, coupled with the associated settled-life, may have just seemed easier than following the herds about.