That negative frequency-dependent selection can promote co-existence of strategies within a population is well established. There is some evidence that negative frequency dependence can also stabilise population size. Here, I will concentrate on one such game, producing and scrounging (PS), which some mammals are known to play. Using a Darwinian dynamics approach, I will show that producing and scrounging in a population can stabilise its abundance and stabilise the abundance of its prey. Furthermore, PS can facilitate the co-existence of two species which consume the same resource. It can also create an equilibrium point in a trophic chain. By contrast, other games which produce negative frequency dependent selection may have less impact. The presence of spite in a population can stabilise its interaction with its prey but this effect does not extend to other species (either competitors or predators). Altruism, on the other hand, can have a destabilising effect on the interaction between a species and its prey.