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Well, there already exists a version of this -- a few orders of magnitude slower -- where some groups of people decide to reproduce faster than other groups.
In real life the limiting factor is often that human children require resources, so too much reproduction may actually harm them by not leaving enough resources per child, so they are later unable to compete with those who received more resources. Another limiting factor is war, often over the resources. And yet another approach is to just let it happen and hope the problem will somehow solve itself, which actually sometimes happens (for example as groups of people get richer, they start valuing comfortable life more, which gets in the way of maximizing the number of their children). Also, sometimes the group actually wins, and then in the future its various subgroups have to compete against each other.
Also, there is the fact of human sexual reproduction, which means that the winning group does not have to exterminate the losing groups; it can also assimilate them. Here is probably the greatest difference compared with the Em scenario, which is like a return to asexual reproduction.