Calling the last game a "Prisoner's Dilemma" is little misleading in this context as the critical difference from the standard Prisoner's Dilemma (the fact that the payoff for (C,D) is the same as for (D,D)) is exactly what makes cousin_it 's (and Nick's) solution work. A small incentive to defect if you know your opponent is defecting defeats a strategy based on committing to defect.