Proposition 6. The strategies which can invade ALL D in a cluster with the smallest value of p are those which are maximally discriminating, such as … - Robert Axelrod

What makes it possible for cooperation to emerge is the fact that the players might meet again. This possibility means that the choices made today not only determine the outcome of this move, but can also influence the later choices of the players. The future can therefore cast a shadow back upon the present and thereby affect the current strategic situation. But the future is less important than the present-for two reasons. The first is that players tend to value payoffs less as the time of their obtainment recedes into the future. The second is that there is always some chance that the players will not meet again. An ongoing relationship may end when one or the other player moves away, changes jobs, dies, or goes bankrupt. For these reasons, the payoff of the next move always counts less than the payoff of the current move.

In addition, TIT FOR TAT was known to be a powerful competitor. In a preliminary tournament, TIT FOR TAT scored second place; and in a variant of that preliminary tournament, TIT FOR TAT won first place. All of these facts were known to most of the people designing programs for the Computer Prisoner's Dilemma Tournament, because they were sent copies of a description of the preliminary tournament. Not surprisingly, many of them used the TIT FOR TAT principle and tried to improve upon it. The striking fact is that none of the more complex programs submitted was able to perform as well as the original, simple TIT FOR TAT.

Proposition 5. ALL D is always collectively stable.