Comment on The Truly Iterated Prisoner's Dilemma

Thu, 12 Apr 2012 19:22:10 GMT

In the case where you know N rounds will occur, you can reason as follows:

1. If one cannot be punished for defection after round x, then one will defect in round x. (premise)

2. If we know what everyone will do in round x, then one cannot be punished for defection in round x. (obvious)

3. There is no round after N, so by (1) everyone will defect in round N.

4. if we know what everyone will do in round x, then we will defect in round x-1, by (1) and (2).

5. By mathematical induction on (3) and (4), we will defect in every round.

If everyone doesn't know what round N is, then the base case of the mathematical induction does not exist.

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