In the first PD simulation I made with five strategies which I got from my friends I applied such a model, albeit with random mutations rather than division of descendants into thirds. The results were not as interesting as I had expected. Only one strategy showed non-trivial optimum (it was basically TfT but defect after turn n and the population made a sort of gaussian distribution around n=85). All other strategies ended up with extremal (and quite obvious) values of the parameter.