¹ E.g., Lord Lindsay of Birker, Scientific Method and International Affairs (Roy Milne Lecture, 1956)Google Scholar, Canberra, Australian Institute of International Affairs, 1957, passim.

² Australian National University, Social Science Monograph No. 9, December 1956; revised for publication as “From Balance to Deterrence: A Theoretical Analysis,” in World Politics, IX (July 1957), pp. 494–529 (citations hereinafter refer to revised version).

³ Kaplan, Morton A., Burns, Arthur L., and Quandt, Richard E., “Theoretical Analysis of the ‘Balance of Power,’” Behavioral Science, V (July 1960), pp. 240–52.Google Scholar

⁴ Driggs, I., “A Monte Carlo Model of Lanchester's Square Law,” Operations Research, IV (April 1956), pp. 148–51.CrossRefGoogle Scholar

⁵ We already distinguish between nuclear and non-nuclear, long-range and short-range forces. See Kaplan, , Burns, , and Quandt, , op.cit., Rules 5–10.Google Scholar

⁶ See Burns, , op.cit., p. 508.Google Scholar

⁷ Ibid.

⁸ Rules 5–10 already allow for “induced” changes in the weapons exchange-rate.

⁹ The unpredictability here referred to does not mean “knowing that there is a probability P that technology will change in such and such a way”; nor “knowing that there is a probability P of there being a probability P that technology will change in such and such a way”; nor any subsequent item in such a series. See Hamblin, C. L., “The Modal ‘Probably’,” Mind, LXVII (April 1959), pp. 234–40CrossRefGoogle Scholar; and Burns, Arthur L., “Inter national Consequences of Expecting Surprise,” World Politics, X (July 1958), pp. 512–36.CrossRefGoogle Scholar

¹⁰ See Burns, , “From Balance to Deterrence,” pp. 495ff.Google Scholar

¹¹ See Burns, A. L., “International Theory and Historical Explanation,” History and Theory (The Hague), 1, No. 1 (December 1960), pp. 55–74.CrossRefGoogle Scholar

¹² Ibid.

¹³ Kahn, Herman and Mann, Irwin, Game Theory, P-1166Google Scholar, The RAND Corporation, July 30, 1957, p. 5.

¹⁴ See Burns, A. L., “NATO and Nuclear Sharing,” in Knorr, Klaus, ed., NATO and American Security, Princeton, N.J., 1959, p. 153Google Scholar, n. 3.

¹⁵ See Hamblin, “The Modal ‘Probably,’ “op.cit., and “Surprises, Innovations, and Probabilities,” May 1958 (manuscript).

¹⁶ See Burns, “International Consequences … ,” passim.

¹⁷ See Hamblin, “Surprises, Innovations, and Probabilities.”

¹⁸ See Brooks, D. L., “Choice of Pay-offs for Military Operations of the Future,” Operations Research, XIII (March-April 1960), pp. 159–68CrossRefGoogle Scholar, where a similar ordinal pro cedure is outlined.

¹⁹ See Kahn, and Mann, , op.ct., pp. 1–2.Google Scholar

²⁰ Op.cit., p. 495.

²¹ Ibid., pp. 509ff. I did the same kind of thing in Power Politics and the Growing Nuclear Club (Policy Memorandum No. 20, Center of International Studies, Princeton University, June 8, 1959), which, like “From Balance to Deterrence,” takes too little account of the sort of particular constraints and facilitations discussed in the opening sections of the present paper.

²² Kaplan and I hope that some hints for an improved statics might emerge from Monte Carlo exploitation of our Game of Power.

²³ Here I was thinking in the first instance of an abstract model—say, of the balance of power. But it is not impossible to do something like this with a historical instance (see following note).

²⁴ For an illustration, and another version of the present argument, see Burns, “Inter national Theory and Historical Explanation.”

²⁵ But I have heard T. C. Schelling liken certain political “warnings” to a threat of mutual Russian roulette.

²⁸ In “On the Rationality Postulates Underlying the Theory of Cooperative Games,” Journal of Conflict Resolution, V (June 1961), pp. 179–96, John C. Harsanyi criticizes Schelling's work along such lines.

²⁷ Ibid.

²⁸ Kaplan, Morton A., System and Process in International Politics, New York, 1957, pp. 17–18.Google Scholar

²⁹ Harsanyi, op.cit.

³⁰ Ibid., pp. 183–84.

³¹ Ibid., p. 179.

³² Ibid., pp. 183–84.

³³ Note, however, that Harsanyi's postulates form a partially self-referring set: (2A) refers to (1), (3), (4), (5), and (6); (2B) refers to (2A), and to (3), (4), (5), and (6), while permitting an exception to (1). Such sets cannot be guaranteed free from the paradoxes of self-reference. Agreed, it may be possible so to restate and reorder Harsanyi's as to remove the self-reference. But intuitively it would seem that the process of reciprocal imputation, which is of the essence of bargaining and strategic situations, somehow has self-reference built in.

³⁴ Ibid., p. 185.

³⁵ I owe this idea to an as yet unpublished paper by Lord Lindsay of Birker, American University, Washington, D.C.

³⁶ Harsanyi, J. C., in “Bargaining in Ignorance of the Opponent's Utility Function” (Cowles Foundation Discussion Paper No. 46, New Haven, Conn., Cowles Commission for Research in Economics, December 11, 1957)Google Scholar, concludes from this kind of situation, among omers, that it is always irrational to enter into bargaining when all parties are ignorant of each other's utility function.

³⁷ See Nogee, Joseph, “The Diplomacy of Disarmament,” International Conciliation, No. 526, January 1960.Google Scholar

³⁸ Ibid., p. 282.

³⁹ E.g., the Soviet delegation's conciliatory attitude toward the French in respect to their proposal for control of vehicles used for delivering nuclear weapons.