  Evolutionary Prisoner's Dilemma games with quenched inhomogeneities in the
spatial dynamical rules are considered. The players following one of the two
pure strategies (cooperation or defection) are distributed on a two-dimensional
lattice. The rate of strategy adoption from a randomly chosen neighbors are
controlled by the payoff difference and a two-value pre-factor $w$
characterizing the players whom the strategy learned from. The reduced teaching
activity of players is distributed randomly with concentrations $\nu$ at the
beginning and fixed further on. Numerical and analytical calculations are
performed to study the concentration of cooperators as a function of $w$ and
$\nu$ for different noise levels and connectivity structures. Significant
increase of cooperation is found within a wide range of parameters for this
dynamics. The results highlight the importance of asymmetry characterizing the
exchange of master-follower role during the strategy adoptions.
