Balanced Strategies for Prisoner's Dilemma

When is a strategy cooperative, yet safe from invasion? A mathematical characterization of such strategies is given, which I call “balanced.” I show that tit-for-tat is balanced, and, in general, a strategy is balanced if and only if its probability of defection on a particular move is sufficiently large relative to the opponent's cumulative score and sufficiently low relative to its own cumulative score.