  We present insights and empirical results from an extensive numerical study
of the evolutionary dynamics of the iterated prisoner's dilemma. Fixation
probabilities for Moran processes are obtained for all pairs of 164 different
strategies including classics such as TitForTat, zero determinant strategies,
and many more sophisticated strategies. Players with long memories and
sophisticated behaviours outperform many strategies that perform well in a two
player setting. Moreover we introduce several strategies trained with
evolutionary algorithms to excel at the Moran process. These strategies are
excellent invaders and resistors of invasion and in some cases naturally evolve
handshaking mechanisms to resist invasion. The best invaders were those trained
to maximize total payoff while the best resistors invoke handshake mechanisms.
This suggests that while maximizing individual payoff can lead to the evolution
of cooperation through invasion, the relatively weak invasion resistance of
payoff maximizing strategies are not as evolutionarily stable as strategies
employing handshake mechanisms.
