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 parame… - Robert Axelrod

So in a non-zero-sum world you do not have to do better than the other player to do well for yourself. This is especially true when you are interacting with many different players. Letting each of them do the same or a little better than you is fine, as long as you tend to do well yourself. There is no point in being envious of the success of the other player, since in an iterated Prisoner's Dilemma of long duration the other's success is virtually a prerequisite of your doing well for yourself.

Proposition 4. For a nice strategy to be collectively stable, it must be provoked by the very first defection of the other player.

4. Teach reciprocity
TIT FOR TAT may be an effective strategy for an egoist to use, but is it a moral strategy for a person or a country to follow? The answer depends, of course, on one's standard for morality. Perhaps the most widely accepted moral standard is the Golden Rule: Do unto others as you would have them do unto you. In the context of the Prisoner's Dilemma, the Golden Rule would seem to imply that you should always cooperate, since cooperation is what you want from the other player. This interpretation suggests that the best strategy from the point of view of morality is the strategy of unconditional cooperation rather than TIT FOR TAT.
The problem with this view is that turning the other cheek provides an incentive for the other player to exploit you. Unconditional cooperation can not only hurt you, but it can hurt other innocent bystanders with whom the successful exploiters will interact later. Unconditional cooperation tends to spoil the other player; it leaves a burden on the rest of the community to reform the spoiled player, suggesting that reciprocity is a better foundation for morality than is unconditional cooperation.