Huh. I finally understand the "logic" that has been espoused in HPMoR, ch 33 ""Precisely," said Harry Potter, his face now turning serious. "We are faced with a true Prisoner's Dilemma..."

What this reminds me of is the logistic equation: dx/dt = x(1-x).

This simple system has two equilibrium points: x = 0, and x = 1. x=0 is unstable - that is, any perturbation will cause the system to veer away from that equilibrium point. x=1 is stable, and any perturbations return to that equilbrium.

Hofstadter says that superrationalists should decide to pick the x=0 (unstable) equilibrium - i.e., cooperate. But any deviation from superrationality, however slight, will cause the equilibrium to collapse into the all-defect equilibrium.