College 11 (deel 3)

This analysis of the one-shot game is in complete contradiction to classical game theory, but follows naturally from the symmetry between the two players:

an optimal strategy must be the same for both players the result must lie on the diagonal of the payoff matrix maximize return from solutions on the diagonal cooperate

[edit] Morality
While it is normally thought that morality must involve the constraint of self-interest, David Gauthier famously argues that co-operating in the prisoners dilemma on moral principles is consistent with self-interest and the axioms of game theory. It's most prudent to give up straightforward maximizing and instead adopt a disposition of constrained maximization, according to which one resolves to cooperate with all similarly disposed persons and defect on the rest. In other words, moral constraints are justified because they make us all better off, in terms of our preferences (whatever they may be). This form of contractarianism claims that good moral thinking is just an elevated and subtly strategic version of plain old means-end reasoning. Those that defect can be predicted because people are not completely opaque.

Douglas Hofstadter expresses a strong personal belief that the mathematical symmetry is reinforced by a moral symmetry, along the lines of the Kantian categorical imperative: defecting in the hope that the other player cooperates is morally indefensible. If players treat each other as they would treat themselves, then off-diagonal results cannot occur.