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

What accounts for TIT FOR TAT's robust success is its combination of being nice, retaliatory, forgiving, and clear. Its niceness prevents it from getting into unnecessary trouble. Its retaliation discourages the other side from persisting whenever defection is tried. Its forgiveness helps restore mutual cooperation. And its clarity makes it intelligible to the other player, thereby eliciting long-term cooperation.

1. Enlarge the shadow of the future
Mutual cooperation can be stable if the future is sufficiently important relative to the present. This is because the players can each use an implicit threat of retaliation against the other's defection-if the interaction will last long enough to make the threat effective. Seeing how this works in a numerical example will allow the formulation of the alternative methods that can enlarge the shadow of the future.

5. Improve recognition abilities The ability to recognize the other player from past interactions, and to remember the relevant features of those interactions, is necessary to sustain cooperation. Without these abilities, a player could not use any form of reciprocity and hence could not encourage the other to cooperate.