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

Cooperation in spatial Prisoner's Dilemma with two types of players for increasing number of neighbors