Restricted connections among distinguished players support cooperation

We study the evolution of cooperation within the spatial prisoner's dilemma game on a square lattice where a fraction of players $\mu$ can spread their strategy more easily than the rest due to a predetermined larger teaching capability. In addition, players characterized with the larger teaching capability are allowed to temporarily link with distant opponents of the same kind with probability $p$, thus introducing shortcut connections among the distinguished. We show that these additional temporary connections are able to sustain cooperation throughout the whole range of the temptation to defect. Remarkably, we observe that as the temptation to defect increases the optimal $\mu$ decreases, and moreover, only minute values of $p$ warrant the best promotion of cooperation. Our study thus indicates that influential individuals must be few and sparsely connected in order for cooperation to thrive in a defection prone environment.