Before revision:  We thereby show that the introduced rule leads to steady state cooperative behavior that is always greater than or equal to the one predicted by  evolutionary stability analysis and discuss relevant implications to natural and artificial systems .
After revision:  We thereby show that the introduced rule leads to steady state cooperative behavior that is always greater than or equal to the one predicted by evolutionary stability analysis of unconditional cooperation. As a consequence, the implementation of our results may go beyond explaining the evolution of cooperation. In particular, they can be directly applied in domains that deal with the development of artificial systems able to adequately mimic reality, such as reinforcement learning .