Proposition 5. ALL D is always collectively stable. - Robert Axelrod

Proposition 2. TIT FOR TAT is collectively stable if and only if, w is large enough. This critical value of w is a function of the four payoff parameters, T; R, P, and S.

Just as important as getting cooperation started were the conditions that allowed it to be sustainable. The strategies that could sustain mutual cooperation were the ones which were provocable.

Proposition 1. If the discount parameter, w, is sufficiently high, there is no best strategy independent of the strategy used by the other player.