 Suggestive as Axelrod's discussion is, it is worth noting that the ideas are not formulated precisely enough to permit a rigorous demonstration of the supremacy of TFT. One doesn't know, for example, the extent of the class of strategies that might have the four properties outlined, or what success criteria might be implied by having them. It is true that if one's opponent is playing TFT (and the shadow of the future is sufficiently large) then one's maximum payoff is obtained by a strategy that results in mutual cooperation on every round. Since TFT is itself one such strategy this implies that TFT forms a nash equilibrium with itself in the space of all strategies. But that does not particularly distinguish TFT, for \(\bDu\), \(\bDu\) is also a nash equilibrium. Indeed, a “folk theorem” of iterated game theory (now widely published — see, for example, Binmore 1992, pp. 373–377) implies that, for any \(p\), \(0 \le p \le 1\) there is a nash equilibrium in which \(p\) is the fraction of times that mutual cooperation occurs. Indeed TFT is, in some respects, worse than many of these other equilibrium strategies, because the folk theorem can be sharpened to a similar result about subgame perfect equilibria. TFT is, in general, not subgame perfect. For, were one TFT player (per impossible) to defect against another in a single round, the second would have done better as an unconditional cooperator.