Cooperation in spatial prisoner's dilemma with two types of players for increasing number of neighbors

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 prefactor (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.