Proposition 3. Any strategy which may be the first to cooperate can be collectively stable only when w is sufficiently large. - Robert Axelrod

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.

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

3. Teach people to care about each other
An excellent way to promote cooperation in a society is to teach people to care about the welfare of others. Parents and schools devote a tremendous effort to teaching the young to value the happiness of others.