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⁴ Ibid., chap. 2.

⁵ The motivation behind this model is discussed at length in Zagare, Frank C., “The Dynamics of Escalation,” Information and Decision Technologies 16, no. 3 (1990)Google Scholar; idem, “NATO, Rational Escalation and Flexible Response,” Journal of Peace Research 4 (November 1992)Google Scholar; and Zagare, Frank C. and Kilgour, D. Marc, “Modeling ‘Massive Retaliation,’” Conflict Management and Peace Science 13, no. 1 (1993)CrossRefGoogle Scholar.

⁶ General deterrence relationships in which a challenger may contemplate a direct nuclear attack are modeled in Kilgour, D. Marc and Zagare, Frank C., “Credibility, Uncertainty, and Deterrence,” American Journal of Political Science 35 (May 1991)CrossRefGoogle Scholar; and Zagare, Frank C. and Kilgour, D. Marc, “Asymmetric Deterrence,” International Studies Quarterly 37 (March 1993)CrossRefGoogle Scholar.

⁷ As R. Harrison Wagner (personal communication, April 24, 1992) points out, we assume that the payoffs at outcome EE are the same, regardless of which player escalates first. We accept the point that players in the real world are likely to prefer escalating first. We make this assumption to gain mathematical tractability. Note its implications: Defender's expected payoffs at Node 2 when it chooses E are underrepresented (because it likely prefers the mutual escalation outcome associated with this choice to the mutual escalation outcome associated with the choice of D); it follows that its expected payoff from choosing (D) at Node 2 is overrepresented. The bias of the model, therefore, is toward overreporting the likelihood of a (Limited-Response) equilibrium that involves the possibility that Defender responds in kind to a challange. As we show below, however, even with this bias, the conditions under which such an equilibrium exists are quite restricted.

⁸ In other words, we assume the choice of D is commensurate with Challenger's initiation at Node 1. Thus, at Node 2, Defender may defect by matching in scope and intensity the actions taken by Challenger to contest the status quo, or it may choose unconstrained actions, such as those associated with waging an all-out war, represented by the escalation alternative (E).

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¹⁰ James D. Fearon's escalation model also has two stages. See Fearon, “Deterrence and the Spiral Model: The Role of Costly Signals in Crisis Bargaining” (Paper presented at the annual meeting of the American Political Science Association, San Francisco, August 30-September 2, 1990). At the first stage, each player is afforded an opportunity to increase its own cost of backing down and, possibly, its credibility; at the second stage, they decide whether or not to fight. Thus, while there are two stages to this model, there is but one mutual conflict outcome. For this reason, we view Fearon's conclusions as extending and complementing our own analysis of one-stage asymmetric deterrence games of incomplete information; see Zagare and Kilgour (fn. 6).

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¹⁵ We believe the opposite assumption is consistent with a policy like massive retaliation that makes no provision for a credible conventional deterrent. For an analysis of this case, see Zagare and Kilgour (fn. 5). For the public justification of flexible response, see Robert S. McNamera, “Address at the Commencement Exercises” (Ann Arbor: University of Michigan, June 16, 1962).

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²¹ As noted in the text, Daalder (fn. 3) argues that the formal definition of flexible response is deliberately vague, in part to accommodate divergent views of how deterrence operates and how forces should be structured. This is the only sense in which pure deterrence is compatible with flexible response.

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²⁶ As detailed in the appendix, some restrictions on r (i.e., Defender's conditional probability that Challenger is seen to be Hard, given that Challenger initiates) also apply under any No-Limited-Response Equilibrium.

²⁷ For a discussion of the impact of specific changes in utilities on the relative locations of the threshold values defining the existence regions of all three forms of NLRE (i.e., d₁, d₂, and c₁), see Zagare and Kilgour (fn. 5).

²⁸ Daalder (fn. 3), 58.

²⁹ Ibid., 46.

³⁰ The Deterrence Equilibrium does not depend on any particular preference relationship. Rather, it exists as long as the players have the required beliefs about each other's action choices, whatever their actual preferences happen to be.

³¹ Zagare and Kilgour (fn. 5).

³² Ibid.

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³⁶ Ibid., 50.

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³⁸ Daalder (fn. 3), 63.

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