  We study co-evolutionary Prisoner's Dilemma games where each player can
imitate both the strategy and imitation rule from a randomly chosen neighbor
with a probability dependent on the payoff difference when the player's income
is collected from games with the neighbors. The players, located on the sites
of a two-dimensional lattice, follow unconditional cooperation or defection and
use individual strategy adoption rule described by a parameter. If the system
is started from a random initial state then the present co-evolutionary rule
drives the system towards a state where only one evolutionary rule remains
alive even in the coexistence of cooperative and defective behaviors. The final
rule is related to the optimum providing the highest level of cooperation and
affected by the topology of the connectivity structure.
