The Evolution of Cooperation in a Generalized Moran Process

In this paper, infinitely repeated prisoner's dilemma game as a benchmark being used to build a new model as the payoff matrix of an evolutionary game dynamics, with the comparative study of game performances between the behavior- pattern “tit for tat” and the behavior-pattern “always defection”, proving that there exists a strictly positive probability, which has a close link with the discount factor, that a single TFT individual can fully invade into a group of ALLD individuals; that is to say, TFT has some kind of evolutionary stability.