This article develops a new methodology for analyzing the arms race between the two superpowers based on an extension of the classic Prisoner's Dilemma game to allow for sequences of moves. The sequence that is formally analyzed depends on a scenario in which each side: (1) possesses an ability to detect what the other side is doing with a specified probability, and (2) pursues a tit-for-tat policy of conditional cooperation—i.e., cooperates if it detects the other side is cooperating, otherwise does not. Given the detection probabilities and the reciprocity norm, the article demonstrates geometrically, when conditional cooperation between the superpowers is rational and, therefore, likely to occur. It discusses policy implications of this analysis for SALT and advances a qualified suggestion for the sharing of intelligence data. It concludes with suggestions for applying the methodology to other games and multistage game scenarios that mirror the dynamics of plausible sequences of moves.