'Raise the stakes' evolves into a defector

Sherratt and Roberts reply — Killingback and Doebeli argue that our cooperative strategy ‘raise the stakes’1 (RTS) can be continually undermined by selection for less generous strategies. They suggest that the “lack of robustness of RTS” arises from our use of a discontinuous strategy. However, this cannot be the case because the instability they report was in their reformulation of our model in continuous terms. Whether a continuous model is “essential” is debatable. Discontinuous strategies can be more realistic, particularly when resources are not infinitely divisible, hence our notion of a minimal non-zero investment of one unit.