1 Brams, Steven J., Superpower Games: Applying Game Theory to Superpower Conflict (New Haven, CT: Yale University Press, 1985), chaps. 1 and 2.
2 Brams, Steven J. and Wittman, Donald, “Nonmyopic Equilibria in 2 × 2 Games,” Conflict Management and Peace Science, vol.6 (Fall 1981), pp.39–62; Kilgour, D. Marc, “Equilibria for Far-sighted Players,” Theory and Decision, vol.16 (March 1984), pp. 135–157; see also Zagare, Frank C., “Limited-Move Equilibria in 2 × 2 Games,” Theory and Decision, vol.16 (January 1984), pp.1–10.
3 Brams, Steven J. and Hessel, Marek P., “Threat Power in Sequential Games,” International Studies Quarterly, vol.28 (March 1984), pp. 15–36.
4 ibid.; the original distinction between compellent and deterrent threats is due to Schelling, Thomas C., Arms and Influence (New Haven, CT: Yale University Press, 1966).
5 The validity of the symmetry condition in the context of Soviet-American conflict is supported by the following statement of an authority on Soviet defense policy: “The answers [to the problems posed by nuclear war and nuclear weapons] the Soviet leaders have arrived at are not very different from those given by Western governments … The Soviet Union has not been able to escape from the threat of nuclear annihilation. Its leaders and its people share our predicament.” Holloway, David, The Soviet Union and the Arms Race (New Haven, CT: Yale University Press, 1983), p.182.
6 For debate on this point, see Frank C. Zagare, “Toward a Reformulation of the Theory of Mutual Deterrence,” International Studies Quarterly, vol. 29 (June 1985); Brams and Hessel, “Threat Power in Sequential Games”; and Brams, Superpower Games, Chap.l.
7 Selten, Reinhard, “Reexamination of the Perfectness Concept for Equilibrium Points in Extensive Games,” International Journal of Game Theory, vol.4 (1975), pp.25–55; see also Shubik, Martin, Game Theory in the Social Sciences: Concepts and Solutions (Cambridge, MA: MIT Press, 1982), pp.265–270.
8 Schelling, Thomas C., The Strategy of Conflict (Cambridge, MA: Harvard University Press, 1960), chap.9.
9 In a more complete dynamic analysis, we show that there is a trajectory or path from either of the Preemption Equilibria to the Deterrence Equilibrium that the player who is preempted can trigger by threatening to move – widi a probability above a, particular threshold – to the mutually worst outcome. Although this player incurs a temporary cost in making this threat, the rational response of the preemptor is to move to the Deterrence Equilibrium, whose dynamic stability would then preclude a rational move away from it. See Brams, Steven J. and Kilgour, D. Marc, “The Path to Stable Deterrence,” Dynamic Models of International Relations, Urs, Luterbacher and Michael, D. Ward, eds., (Boulder, CO: Lynne Rienner, 1985). A game analogous to the Deterrence Game, but based on Prisoners' Dilemma rather than Chicken, permits the players to move from the Pareto-inferior “Escalation Equilibrium” to the Pareto-superior “Deescalation Equilibrium,” that is costless to the player who initiates a move from the Escalation to the Deescalation Equilibrium. See Brams, Steven J. and Kilgour, D. Marc, “Rational Deescalation” (mimeographed, 1985).
10 Brams, Superpower Games, chap.l.
11 Bracken, Paul, The Command and Control of Nuclear Weapons (New Haven, CT: Yale University Press, 1983). Gauthier claims that such precommitments are not necessary to deter aggression, but threats which are not credible are empty, and empty threats invite attack. His calculus of deterrence, we believe, is sensible only when his retaliator's threats will assuredly be implemented because of precommitments. See Gauthier, David, “Deterrence, Maximization, and Rationality,” Ethics, vol.94 (April 1984), pp.474–495.
12 Brams, Superpower Games, pp.45–46.