Directed reciprocity subverts cooperation in highly adaptive populations

We examine the generally accepted hypothesis that directed reciprocity is a powerful driver for cooperation. To do so, we consider a framework where agents situated on a circle network interact with their neighbors and have the choice to be egoistic, altruistic, or partially cooperative. We study the interaction between reciprocity, the likelihood that an agent reproduces value to the neighbor who has recently produced value for the agent, and inertia, the tendency of agents to repeat their previous choices even if other strategies are more successful. On the basis of extensive simulations, we conclude that for high levels of inertia, reciprocity enhances cooperation, while for low levels of inertia reciprocity rather subverts cooperation. For intermediate levels of inertia, we find a U-shaped effect. Reciprocity therefore interacts with the level of inertia in a non-monotonic fashion.