  We study a spatial two-strategy (cooperation and defection) Prisoner's
Dilemma game with two types ($A$ and $B$) of players located on the sites of a
square lattice. The evolution of strategy distribution is governed by iterated
strategy adoption from a randomly selected neighbor with a probability
depending on the payoff difference and also on the type of the neighbor. The
strategy adoption probability is reduced by a pre-factor ($w < 1$) from the
players of type $B$. We consider the competition between two opposite effects
when increasing the number of neighbors ($k=4$, 8, and 24). Within a range of
the portion of influential players (type $A$) the inhomogeneous activity in
strategy transfer yields a relevant increase (dependent on $w$) in the density
of cooperators. The noise-dependence of this phenomenon is also discussed by
evaluating phase diagrams.
