1 See Brams, Steven J. and Kilgour, D. Marc, “Threat Escalation and Crisis Stability: A Game-Theoretic Analysis,” American Political Science Review 81 (1987), 833–50.CrossRefGoogle Scholar

2 The de-escalation model which appears in Brams, Steven J. and Kilgour, D. Marc, “Winding Down if Preemption or Escalation Occurs: A Game-Theoretic Analysis,” Journal of Conflict Resolution 31 (1987), 547–72CrossRefGoogle Scholar, is not based on the Threat Game and therefore is not discussed in this article.

4 Brams and Kilgour, “Threat Escalation and Crisis Stability.”

5 An interesting critique of game-theoretic and other models of crisis bargaining appears in Morgan, T. Clifton, “A Spatial Model of Crisis Bargaining,” International Studies Quarterly 28 (1984). 408–14.CrossRefGoogle Scholar

6 An argument in favour of the Prisoner's Dilemma game as a superior model of deterrence appears in Zagare, Frank, “Toward a Reformulation of the Theory of Mutual Deterrence,” International Studies Quarterly 29 (1985), 155–69.CrossRefGoogle Scholar However, the equilibrium of that game, in which both players defect, is not consistent with the record of mutually assured destruction. The act of each player defecting corresponds with a nuclear exchange, which has not occurred. Furthermore, the outcome of mutual non-co-operation does not produce the worst payoff for each player in a Prisoner's Dilemma game. A nuclear exchange, as opposed to experiencing unilateral coercion in crisis bargaining, should result in the lowest utility level for a target state.

7 Brams and Kilgour, “Threat Escalation and Crisis Stability,” 835.

8 Ibid.

9 Ibid., and Brams, Steven J. and Kilgour, D. Marc, “Optimal Threats,” Operations Research 35 (1987), 524–36.CrossRefGoogle Scholar

10 This description of the Threat Game is based on Brams and Kilgour, “Optimal Threats.”

11 The final position, in turn, represents the preplay position of the next crisis involving the superpowers. In other words, as the crisis conditions fade away during the process of de-escalation, the final position gradually takes on the role of the preplay position for the next iteration of the Threat Game, a new crisis.

12 The outcomes on the corners are specified in Brams and Kilgour, “Threat Escalation and Crisis Stability,” 836.

14 Ibid.

15 Ibid., 840.

16 Ibid., 842.

17 Ibid., 845–48.

18 Ibid.

19 An obvious line of criticism at this point is derived from Allison's analysis of the unitary rational actor assumption: can the US and the USSR be regarded as players in a two-“person” game? See Allison, Graham T., Essence of Decision: Explaining the Cuban Missile Crisis (Boston: Little, Brown, 1971).Google Scholar However, McGinnis has argued effectively that sustained competition between states creates a setting in which the rational actor axiom is most closely approximated. See McGinnis, Michael, “Domestic Political Competition and the Unitary Rational Actor Assumption: Models of Security Rivalries,” paper presented at the annual meeting of the International Studies Association, St. Louis, Missouri, 1988.Google Scholar

20 Organski, A. F. K. and Kugler, Jacek, The War Ledger (Chicago: University of Chicago Press, 1980).Google Scholar

21 Kolkowicz, for example, characterized the Soviet view of the geo-strategic status quo as less favourable than that of the US. While the ordering of payoffs would be preserved, the emphasis on stability—so prevalent in the West—would be much lower. See Kolkowicz, Roman, “The Soviet Union: The Elusive Adversary,” in Kolkowicz, Roman and Mickiewicz, Ellen Propper (eds.), The Soviet Calculus of Nuclear War (Lexington, Mass.: Lexington Books, 1986), 1–24.Google Scholar

22 Of course, among the corner payoffs, the utilities for all but c ₁, could be allowed to show variation from one crisis to the next. In testing the revised model, however, it will be assumed that the corner payoffs are constant across cases.

23 A supergame analysis of Chicken by Ward, for example, suggests that a reputation for toughness will have different implications depending on the complexity of the game. See Ward, Hugh, “The Risks of a Reputation for Toughness: Strategy in Public Goods Provision Problems Modelled by Chicken Supergames,” British Journal of Political Science 17 (1987), 23–52.CrossRefGoogle Scholar

24 It will be demonstrated later that, for all cases included in the subsequent analysis, Equation (9) points to the need for an escalating threat in order to achieve crisis stability. In cases for which the inequality in Equation (9) is reversed, the independent variables in Propositions 4 and 5 are presumed to have the opposite impact. For example, in Proposition 4, a smaller difference between s and t would be expected to facilitate crisis stability and therefore produce a higher level of satisfaction for the initially more co-operative player. The properties of the Threat Game which account for this reversal of causal impact are explained thoroughly in Brams and Kilgour, “Threat Escalation and Crisis Stability.”

25 Ibid., 842–43.

26 Ibid., 843.

27 Brecher, Michael, Wilkenfeld, Jonathan et al., Crises in the Twentieth Century, Vol. 1: Handbook of International Crises (Oxford: Pergamon Press, 1988), 3.Google Scholar For a more extensive explanation of intra-war crises, in which international crises take place within the context of an ongoing war, see Ibid., 95.

28 The conditions which define an international crisis are derived at length in Brecher, Michael and Yehuda, Hemda Ben, “System and Crisis in International Politics,” Review of International Studies 11 (1985), 17–36.CrossRefGoogle Scholar Based on those defining conditions, the ICB Project has compiled data for each international crisis for 28 variables that are grouped along seven crisis dimensions: breakpoint/exit point (or trigger/termination), crisis management techniques, great power/superpower activity, international organization involvement, outcome and severity. Two coders independently gathered data for each case under the supervision of a senior ICB investigator; inter-coder reliability was. 85.

29 This definition forms the basis for 627 cases from 1929 through 1979 and is derived from Brecher, Michael, “Toward a Theory of International Crisis Behaviour: A Preliminary Report,” International Studies Quarterly 21 (1977), 43–44.CrossRefGoogle Scholar

30 It could be argued that even prior to the first trigger, the adversaries are not engaged in full co-operation. But the preplay position represents co-operation in a more narrow sense than is usually understood, without connotations of active or positive collaboration. For example, superpower relations prior to the Berlin Blockade were characterized for months by provocative acts which pertained to reparation payments, printing of currency in the Eastern zone and the Allied Control Commission. See Oneal, John R., Foreign Policy Making in Times of Crisis (Columbus, Ohio: Ohio State University Press, 1982), 225–37.Google Scholar However, co-operation still existed because none of these early actions had sufficient intensity to trigger a crisis. Thus the point (1, 1) on the unit square represents an ongoing conflict below the crisis level.

31 Brams and Kilgour, “Threat Escalation and Crisis Stability,” 835.

32 There are cases in which the trigger and major response occur in close proximity. However, of the cases that appear in Table 1, the average time lag is greater than one month.

33 Brams and Kilgour explicitly acknowledge that the “route by which the final position is attained from the preplay and initial positions may be relevant but will not be modeled here.” Thus the model of crisis stability is designed not to be a description of the process, but instead to operate as an explanation of the outcome (Brams and Kilgour, “Threat Escalation and Crisis Stability,” 848–49).

34 With time, the final position takes on the role of the preplay position for a new round of interaction. At some point, the final position no longer is perceived as representing a crisis. For example, the US eventually accepted the Berlin Wall as part of the geo-strategic terrain of Europe although the initial construction of the Wall had created a threat to basic values, high probability of military hostilities and finite time for response. By October 1961, the Wall no longer had that impact on the US, just as the tension generated by the non-violent military actions of the US receded for the Soviets. When the crisis conditions terminated, the players effectively returned to their preplay positions.

35 There are a few cases to consider in which one superpower simultaneously threatens both the other superpower and a client state. In such instances it is appropriate to treat the incident as one case directly involving the superpowers. The response by the threatened superpower is assumed to include its client state as well. For a more general discussion of coding rules for crisis initiation, see James, Patrick, Crisis and War (Montreal: McGill-Queen's University Press, 1988), 51–54.Google Scholar

36 An extensive review of the literature on nuclear deterrence derived the criteria summarized here. See James, Patrick and Harvey, Frank, “Nuclear Deterrence Theory: The Record of Aggregate Testing” (unpublished manuscript, McGill University, 1988).Google Scholar

37 The period prior to 1949 created a setting for the multiple iterations of the Threat Game. Soviet fears of encirclement and invasion by the West were entrenched following 1917, while the period from 1945 until 1948 established within the US a fear of Soviet expansionism. Mutual co-operation in the Threat Game, represented by the preplay position at (1, 1), thus refers to the absence of crisis and not to an atmosphere of trust and active collaboration.

38 Obviously (r ₁, c_l) has different connotations in more recent years when the superpowers possess far greater destructive capacity than previously. However, the impact of even one crude nuclear weapon would be viewed as a catastrophe by a target state and would be much more damaging, for example, than defeat in a battle involving conventional forces. Prior to the development of intercontinental delivery systems, a strike by the USSR against Western Europe would be regarded as approximately equivalent to an attack on the US itself. In sum, the increased tonnage and accuracy of nuclear weapons (few or many in number) are essential to the superpower Threat Game presented by Brams and Kilgour.

39 Kugler, Jacek, “Terror without Deterrence: Reassessing the Role of Nuclear Weapons,” Journal of Conflict Resolution 28 (1984), 474.CrossRefGoogle Scholar

40 See Patrick James, “Rational Retaliation: Superpower Response to Crisis, 1948–1979,” Public Choice, forthcoming. It could be argued that the USSR might place a higher value on the status quo in some cases. After all, the US has initiated crises that threatened to alter the status quo in ways that challenged the geo-strategic position of the USSR (for example, the mining of Haiphong Harbour in 1972). However, the intensity of preference for preserving the status quo is less for the USSR than the US when the latter is on the defensive. The gap between winning and the status quo is 1/3 for the USSR and 1/4 for the US.

41 It is possible that every national leader will attach a very high value to the status quo, c ₃ or r ₃, perhaps close to 1.0. However, the occurrence of international crises suggests that the USSR and the US sometimes are willing to risk war in order to obtain concessions (although intending to return the situation to the status quo). Thus the lower values attached to the status quo by the USSR and the US, 2/3 and 3/4 respectively, are viable choices based on past performance.

42 It might be suggested that identifying the act of non-co-operation which initiates an international crisis requires problematic value judgments. However the ICB Project coding procedures, described above in footnote 28, minimized problems of reliability.

43 With respect to triggering acts, it is obvious that neither co-operation nor a lack of action (the final two scale points) can trigger a crisis. However, superpower rivalry is assumed to be in progress at all times. Each of these non-threatening forms of behaviour may thus be regarded as a choice available to the players at any given time.

44 On the ICB categories and coding procedures, see Brecher, Wilkenfeld et al., Crises in the Twentieth Century.

45 The scale in Table 2 is considered to be at the ratio level for two reasons: first, it has a fixed zero point (nuclear strike) which represents the absence of co-operation; and second, the differences in intensity among scale points are meaningful in proportion to each other. Leaving aside for the moment questions about measurement error, a comparison of indirect minor clashes (0.39) with political acts (0.80) is taken to represent approximately twice as much pre-emption in the first instance as in the second. Further research is required to determine inaccuracies in this initial effort toward scaling techniques of bargaining.

46 The tau b statistic measures the percentage reduction in error in predicting categories of the dependent variable. For example, if tau b = .25, then the independent variable in question produces a 25 per cent reduction in error when predicting categories of the dependent variable.

47 Michael Nicholson, personal communication to the authors, 1988.

48 Wagner, R. Harrison, “Deterrence and Bargaining,” Journal of Conflict Resolution 26 (1982), 356.CrossRefGoogle Scholar

49 For this comparative analysis, see James, Patrick and Harvey, Frank, “Optimal Threats: Superpower Crisis Behaviour, 1948–1985” (unpublished manuscript, McGill University, 1989).Google Scholar

50 See Jervis, Robert, Lebow, Richard Ned and Stein, Janice, Psychology and Deterrence (Baltimore: Johns Hopkins University Press, 1985)Google Scholar; Jervis, Robert, Perception and Misperception in International Politics (Princeton: Princeton University Press, 1976)Google Scholar; and Jervis, Robert, “Deterrence and Perception,” in Matthews, R. O., Rubinoff, A. G. and Stein, J. G. (eds.), International Conflict and Conflict Management (Scarborough: Prentice-Hall, 1984), 31–43.Google Scholar

51 Jervis, Lebow and Stein, Psychology and Deterrence, 33.