Pavlov. Cooperate if both villages made the same move
    last year. Attack if you made different moves.

    Equalizer. Choose to cooperate or attack so that both
    villages have equal expected grain yield in the long run.

    Extorter. Attack in such a way that your village’s grain
    yield is always higher than your opponent’s, even if this
    means total grain yield by both villages collapses.

    Then there are advanced strategies, colluders that use
    coded sequences of cooperation and attacks to recognize
    each other and form hierarchies. Never mind those for
    now.

The most Human strategy is some variant of tit for tat: tend to cooperate, but do unto others as they do to you. Start nothing. But if you are hit, hit back hard. Hit back harder each time.

So you punish the other village for attacking. You counterattack. Unwilling to walk away from a war they’ve already spent blood on, the other village attacks for the next two years in a row. A cycle of war begins.

If we take “A” to mean cooperating, and “X” to mean attacking (defecting), and both villages are playing tit for tat, the two villages’ behavior over the years will look like this:

    AAAAAAAAAAAAAXXXXXXXXXX
    XXXXXXXXXXXXXXXXXXXXXXXXXX

    AAAAAAAAAAAAXXXXXXXXXXX
    XXXXXXXXXXXXXXXXXXXXXXXXXX

They are now trapped in an infinite war.

Let’s say that the villages’ yearly grain production plunges from 1,800 bushels to 1,200 bushels in the first year of war, to 1,000 bushels each year afterwards. Yet neither side can break out of the cycle of retaliation.

The only way out is a moment of grace. Cooperation, spontaneously and for no reason, after 20 years of war. Forgiveness without cause. Unilateral mercy. Declaring peace. This is the value of forgetting. Forget they hurt you. Forget what’s rational. Do what’s right.