Winding Down if Preemption or Escalation Occurs

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Abstract
Game-theoretic models of deterrence and escalation, based on Chicken and Prisoners' Dilemma, are developed in which two players can initially choose any level of preemption in a crisis (Deterrence Game) or escalation in an arms race (Deescalation Game). The greater this level, the more likely an opponent will interpret this choice as a noncooperative action and retaliate. Given that both players make noncooperative choices in these games—either initially or in retaliation—a probability of winding down is postulated whereby the playes can escape either the mutually worst outcome in the Deterrence Game (which becomes the Winding-Down Game) or the mutually next-worst outcome in the Deescalation Game (which becomes the Arms-Reduction Game). In both games, as the probability of winding down increases, the threat of retaliation must also increase—and at an increasing rate—to preserve the stability of mutual deterrence and mutual deescalation. Implications of these findings, especially for encouraging mutual cooperation between the superpowers, via both deterrence and defense (“Star Wars”), are discussed.

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