Based on the game "Prisoners' Dilemma," a game-theoretical model of the arms race suitable for postsecondary level mathematics and/or political science students is developed in which two players can initially choose any level of arms development. The purpose of the game is to show under what conditions deescalation rather than escalation is a rational response to the burdens that an unrestricted arms race imposes on both sides. The strategic problem that the players face is to choose both an initial level of action (with an associated escalation probability) and a subsequent level of response (with an associated retaliation probability). The higher the level of arming, the greater the probability that the choice will be viewed as escalatory. A matrix representation and the rules of the game are provided in the text which also explains the payoffs, strategic choices, and their interpretations. Quantitative, sequential choices define the game, which contains an Escalation Equilibrium analogous to the non-cooperative outcome in "Prisoners' Dilemma," The game also contains a Deescalation Equilibrium, which is analogous to the cooperative outcome in "Prisoners' Dilemma," except that it is stable. Separate sections provide an introduction, a description of "Prisoners' Dilemma" in relation to the superpower arms race, a discussion of the Deescalation Game and suggestions for rational play, and conclusions. An appendix presenting the details of the game's analysis and calculations of the players maximum strategies and values concludes the paper. (LH)