Inefficient stage Nash is not stable

It is shown that, in infinitely-repeated games between two arbitrarily patient players, strategy profiles with inefficient pure stage-Nash continuations are not strategically stable (Kohlberg and Mertens, 1986). By contrast, a set of strategy profiles similar to the Prisoners' Dilemma's “perfect tit-for-tat” is “uniformly robust to perfect entrants” (Swinkels, 1992), and hence contains a strategically stable set. Moreover, this set satisfies iterated dominance and a version of forward induction, whilst its stable subset is admissible.