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 randomly chosen neighbors is 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 ν 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 ν 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.
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