¹ See, for instance, Barton, John H. and Weiler, Lawrence D., eds., International Arms Control: Issues and Agreements (Stanford, CA: Stanford University Press, 1976)Google Scholar; George, Alexander L. and Smoke, Richard, Deterrence in American Foreign Policy (New York: Columbia University Press, 1974)Google Scholar; Morgan, Patrick M., Deterrence: A Conceptual Analysis, 2d ed. (Beverly Hills, CA: Sage, 1983)Google Scholar; Jervis, Robert, “Deterrence Theory Revisited,” World Politics 31 (January 1979), 289–324CrossRefGoogle Scholar.

² See, inter alia, Brams, Steven J., Superpower Games (New Haven, CT: Yale University Press, 1985)CrossRefGoogle Scholar; Brams, Steven J. and Kilgour, D. Marc, Game Theory and National Security (New York: Basil Blackwell, 1988)Google Scholar; Mesquita, Bruce Bueno de, The War Trap (New Haven, CT: Yale University Press, 1981)Google Scholar; Mesquita, Bruce Bueno de, “The War Trap Revisited,” American Political Science Review 79 (March 1985), 156–73Google Scholar; Mesquita, Bruce Bueno de and Riker, William H., “An Assessment of the Merits of Selective Nuclear Proliferation,” Journal of Conflict Resolution 26 (June 1982), 283–306CrossRefGoogle Scholar; Fraser, Niall M. and Hipel, Keith, Conflict Analysis: Models and Resolution (New York: North-Holland, 1984)Google Scholar; Gauthier, David, “Deterrence, Maximization, and Rationality,” Ethics 94 (April 1984), 474–95CrossRefGoogle Scholar; Morgan, T. Clifton, “A Spatial Model of Crisis Bargaining,” International Studies Quarterly 28 (December 1984), 407–26CrossRefGoogle Scholar; Morrow, James D., “A Continuous-Outcome Expected Utility Theory of War,” Journal of Conflict Resolution 27 (September 1985), 473–502CrossRefGoogle Scholar; Morrow, James D., “A Spatial Theory of International Conflict,” American Political Science Review 80 (December 1986), 1131–50CrossRefGoogle Scholar. Powell, Robert, “Crisis Bargaining, Escalation, and MAD,” American Political Science Review 81 (September 1987), 717–35CrossRefGoogle Scholar; Powell, Robert, “Nuclear Brinkmanship with Two-Sided Incomplete Information,” American Political Science Review 82 (March 1988), 156–78CrossRefGoogle Scholar; Wagner, R. Harrison, “Deterrence and Bargaining,” Journal of Conflict Resolution 26 (June 1982), 329–58CrossRefGoogle Scholar; Wagner, R. Harrison, “The Theory of Games and the Problem of International Cooperation,” American Political Science Review 77 (June 1983) 330–46CrossRefGoogle Scholar; R. Harrison Wagner, “The Theory of Games and the Cuban Missile Crisis” (Paper presented at the Annual Meeting of the American Political Science Association, Chicago, IL, September 3–6, 1987); Zagare, Frank C., “Toward a Reformulation of the Theory of Mutual Deterrence,” International Studies Quarterly 29 (June 1985), 155—69CrossRefGoogle Scholar; and Zagare, Frank C., The Dynamics of Deterrence (Chicago: University of Chicago Press, 1987)Google Scholar.

³ Morgan (fn. 1), 13.

⁴ Simon, Herbert A., “From Substantive to Procedural Rationality,” in Latsis, S. J., ed., Method and Appraisal in Economics (Cambridge: Cambridge University Press, 1976)Google Scholar.

⁴⁵ Verba, Sidney, “Assumptions of Rationality and Non-rationality in Models of the International System,” in Knorr, Klaus and Verba, Sidney, eds., The International System: Theoretical Essays (Princeton, NJ: Princeton University Press, 1961), 95Google Scholar.

⁶ Rivera, Joseph de, The Psychological Dimension of Foreign Policy (Columbus, OH: Merrill, 1968)Google Scholar; Lebow, Richard Ned, Between Peace and War: The Nature of International Crisis (Baltimore, MD: The Johns Hopkins University Press, 1981)Google Scholar; and Steinbruner, John, “Beyond Rational Deterrence: The Struggle for New Conceptions,” World Politics 28 (January 1976), 223–45CrossRefGoogle Scholar.

⁷ Allison, Graham T., Essence of Decision: Explaining the Cuban Missile Crisis (Boston: Little, Brown, 1971)Google Scholar.

⁸ Mandel, Robert, “Psychological Approaches to International Relations,” in Hermann, Margaret G., ed., Political Psychology: Contemporary Problems and Issues (San Francisco, CA: Jossey-Bass, 1986), 251Google Scholar.

⁹ Of course, this paradigm shift of sorts is most properly traced to the pioneering work of Snyder, Richard C., Bruck, H. W., and Sapin, Burton, eds., Foreign Policy Decision-Making: An Approach to the Study of International Politics (New York: Free Press, 1962)Google Scholar. For this argument see Rosenau, James N., “The Premises and Promises of Decision-Making Analysis,” in Charlesworth, James C., ed., Contemporary Political Analysis (New York: Free Press, 1967)Google Scholar, and White, B. P., “Decision-making Analysis,” in Taylor, Trevor, ed., Approaches and Theory in International Relations (London: Longman, 1978)Google Scholar.

¹⁰ Luce, Duncan R. and Raiffa, Howard, Games and Decisions: Introduction and Critical Survey (New York: Wiley, 1957), 50Google Scholar.

¹¹ Allison (fn. 7), 246.

¹² Tversky, Amos and Kahnerman, Daniel, “The Framing of Decisions and the Psychology of Choice,” Science, 30 January 1981, 453–58CrossRefGoogle Scholar.

¹³ Daniel Ellsberg, “The Theory and Practice of Blackmail,” lecture at the Lowell Institute, Boston, MA, March 10, 1959; reprinted in Young, Oran R., ed., Bargaining: Formal Theories of Negotiation (Urbana, IL: University of Illinois Press, 1975), 347Google Scholar.

¹⁴ It may be true, as Robert Jervis writes in “Realism, Game Theory, and Cooperation,” that “by taking preferences as given, we beg … the most important question on how they are formed” (World Politics 40 [April 1988], 317–49, at 324). But this does not mean that other questions are unimportant. Indeed, as I argue below, meaningful scientific progress depends upon knowing both the sources of preferences and their strategic implications. Understanding how the world works should not always be depicted as a zero-sum game between competing groups of theorists, or as an either/or choice about research foci and methods.

¹⁵ This is not to suggest that normative questions are outside the scope of legitimate inquiry. It is simply to say that, in general, instrumentalists have used this concept for purposes that are different from, though not necessarily inconsistent with, more traditional normative concerns.

¹⁶ Lebow (fn. 6).

¹⁷ E.g., Samuelson's theory of revealed preferences. Samuelson, Paul A., “A Note on the Pure Theory of Consumer's Behaviour,” Economica 5 (February 1938), 61–71CrossRefGoogle Scholar.

¹⁸ E.g., Snyder, Glenn H. and Diesing, Paul, Conflict Among Nations: Bargaining, Decision Making and System Structure in International Crises (Princeton, NJ: Princeton University Press, 1977), chap. 5Google Scholar.

¹⁹ See, for example, Bueno de Mesquita's expected utility model developed in The War Trap (fn. 2) and “The War Trap Revisited” (fn. 2), which postulates decision makers who, by way of their risk functions, distort objective reality.

²⁰ See Stein, Arthur A., “When Misperception Matters,” World Politics 34 (July 1982), 505–26CrossRefGoogle Scholar, for an example of such a merger.

²¹ Selten, Reinhard, “A Re-examination of the Perfectness Concept for Equilibrium Points in Extensive Games,” International Journal of Game Theory 4, No. 1 (1975), 25–55CrossRefGoogle Scholar.

²² Nash, John, “Non-cooperative Games,” Annals of Mathematics 54 (September 1951), 286–95CrossRefGoogle Scholar.

²³ This is why a game theorist would object to Karl W. Deutsch's suggestion that each player in a Chicken game choose his cooperative (C) strategy. Since the resulting outcome (3,3) is not an equilibrium outcome, it is inconsistent with the instrumentalists' definition of rationality. See Deutsch, , The Analysis of International Relations, 3d ed. (Englewood Cliffs, NJ: Prentice-Hall, 1988), 149–50Google Scholar.

²⁴ Harsanyi, John C., “Advances in Understanding Rational Behavior,” in Butts, R. E. and Hintikka, J., eds., Foundational Problems in the Special Sciences (Dordrecht, Holland: D. Rei del, 1977)Google Scholar.

²⁵ A dominant strategy provides at least as good an outcome for a player as any other, no matter what strategy the other player(s) in the game select. For a further discussion of this and related concepts, see Zagare, Frank C., Game Theory: Concepts and Applications (Beverly Hills, CA: Sage, 1984)CrossRefGoogle Scholar.

²⁶ Harsanyi (fn. 24), 332.

²⁷ Achen, Christopher H. and Snidal, Duncan, “Rational Deterrence Theory and Comparative Case Studies,” World Politics 41 (January 1989), 143–69CrossRefGoogle Scholar.

²⁸ The irony of this misunderstanding is hard to miss.

²⁹ Downs, George W., “The Rational Deterrence Debate,” World Politics 41 (January 1989), 225–37CrossRefGoogle Scholar.

³⁰ Jervis, Robert, “Perceiving and Coping with Threat,” in Jervis, Robert, Lebow, Richard Ned, and Stein, Janice Gross, eds., Psychology and Deterrence (Baltimore, MD: The Johns Hopkins University Press, 1985), 33Google Scholar.

³¹ Achen, Christopher H., “A Darwinian View of Deterrence,” in Kugler, Jacek and Zagare, Frank C., eds., Exploring the Stability ofDeterrence (Denver: University of Denver School of International Studies, 1987)Google Scholar; Zagare (fn. 2, 1987). This is why Robert Jervis, “Introduction: Approach and Assumptions,” in Jervis, Lebow, and Stein (fn. 30), 6, correctly, finds that “many events present unexplained puzzles for standard deterrence theory.” For an attempt to explain some of these inconsistencies, see Jacek Kugler and Frank C. Zagare, “The Long-term Stability of Deterrence,” International Interactions 15, Nos. 3 and 4 (1989), 253–75.

³² Brodie, Bernard, ed., The Absolute Weapon: Atomic Power and World Order (New York: Harcourt Brace, 1946), 76Google Scholar.

³³ See, for example, Kaufmann, William, “The Requirements of Deterrence,” in Kaufmann, William, ed., Military Policy and National Security (Princeton, NJ: Princeton University Press, 1956)Google Scholar.

³⁴ See, inter alia, Jervis (fn. i), 291; Rapoport, Anatol, Strategy and Conscience (New York: Harper and Row, 1964), 116Google Scholar; Hopkins, Raymond F. and Mansbach, Richard W., Structure and Process in International Politics (New York: Harper and Row, 1973), 368–69Google Scholar; Brams, Steven J., Game Theory and Politics (New York: Free Press, 1975)Google Scholar; Brams (fn. 2); Brams and Kilgour (fn. 2); Schelling, Thomas C., The Strategy of Conflict (Cambridge: Harvard University Press, 1960)Google Scholar; and Schelling, Thomas C., Arms and Influence (New Haven, CT: Yale University Press, 1966)Google Scholar.

³⁵ Jervis, Robert, The Illogic of American Nuclear Strategy (Ithaca, NY: Cornell University Press, 1984), 19Google Scholar.

³⁶ Achen (fn. 31).

³⁷ There is actually a third option. For their part, micro-level theorists have attempted to recast the theory by placing it on a firmer psychological foundation. This, in my opinion, is constructive, but not necessarily at odds with the second alternative.

³⁸ Ellsberg (fn. 13).

³⁹ Schelling (fn. 34, 1960, 1966).

⁴⁰ For a critique of the logical foundations of the earlier theoretical literature, see Zagare (fn. 2, 1987), chap. 1.

⁴¹ Schelling (fn. 34, 1960, 1966); Ellsberg (fn. 13); Snyder, Glenn H., “Crisis Bargaining,” in Hermann, Charles F., ed., International Crises: Insights From Behavioral Research (New York: Free Press, 1972)Google Scholar; Robert Jervis, “Bargaining and Bargaining Tactics,” in J. Roland Pennock and John W. Chapman, eds., Coercion, Nomos XIV, Yearbook of the American Society for Political and Legal Philosophy (Chicago: Aldine-Atherton, 1972); Kahn, Herman, On Thermonuclear War (Princeton, NJ: Princeton University Press, 1960)Google Scholar.

⁴² Or, as many have noted, with a “sufficiently” high probability.

⁴³ Gauthier (fn. 2).

⁴⁴ Brams and Kilgour (fn. 2).

⁴⁵ Schelling (fn. 4, 1960), 26.

⁴⁶ Gauthier (fn. 2), 494, to his credit, maintains logical consistency by admitting other possible commitment strategies. “Rational nations,” he writes, “recognizing the need to seek peace and follow it given the costs of war, can unilaterally renounce the first use of nuclear weapons and thereby end all strike policies.” But if this prescription strikes the reader as hopelessly naive, then so should the prescriptions of deterrence theory. Each rests upon self-abnegating choices. Brams and Kilgour assume the same when they allow each player to commit, albeit probabilistically, to a level of nonpreemption.

⁴⁷ Powell (fn. 2, 1987).

⁴⁸ Powell's model thereby provides a formalization of Schelling's “strategy-that-leaves-something-to-chance” (fn. 34, 1960).

⁴⁹ When information is complete, deterrence is never stable. The player with the highest “effective” resolve simply escalates and wins. A similar conclusion is found in Zagare (fn. 2, 1987). 53–54.

⁵⁰ Gray, Colin S., “Nuclear Strategy: The Case for a Theory of Victory,” International Security 4 (Summer 1979), 54–87CrossRefGoogle Scholar; Nitze, Paul H., “Deterring Our Deterrent,” Foreign Policy 25 (Winter 1976–1977), 195–210CrossRefGoogle Scholar; Wohlstetter, Albert, “The Delicate Balance of Terror,” Foreign Affairs 37 (January 1959), 211–35CrossRefGoogle Scholar.

⁵¹ Why, for instance, don't the Soviets simply invade western Europe, given that each side's strategic arsenal is mutually deterred?

⁵² Maxwell, Stephen, Rationality in Deterrence, Adelphi Paper No. 50 (London: Institute for Strategic Studies, 1968)Google Scholar.

⁵³ Achen (fn. 31), 92.

⁵⁴ Powell (fn. 2, 1987) 725, admits as much when he writes “One might object that requiring the states' strategies to be sequentially rational and then relying on Nature to impose the irrational sanction does not really solve the credibility problem. I agree with this criticism.” Powell goes on to note, however, that “it is important to realize that this is not so much a criticism of the model as it is a fundamental criticism of the way that the strategy-that-leaves-something-to-chance has attempted to overcome the credibility problem. The model only exposes this weakness.” I concur with this observation. One of the unrecognized advantages of formal models like Powell's is that they facilitate the exposure of underlying assumptions to careful scrutiny.

⁵⁵ Young, Oran R., The Politics of Force: Bargaining During International Crises (Princeton, NJ: Princeton University Press, 1968), 218Google Scholar.

⁵⁶ Ellsberg (fn. 13), 357.

⁵⁷ Zagare (fn. 2, 1987).

⁵⁸ Ellsberg (fn. 13), 358.

⁵⁹ Wagner (fn. 2, 1982), 343.

⁶⁰ Specifically, if each player prefers executing the deterrent threat, nuclear deterrence is stable; if neither player has a credible threat, it is not; and if only one player's retaliatory threat is credible, that player wins (Zagare [fn. 2, 1987], chap. 2).

⁶¹ D. Marc Kilgour and Frank C. Zagare, “Uncertainty and Deterrence” (Paper delivered at the Annual Meeting of the American Political Science Association, Atlanta, GA, August 31-September 3, 1989).

⁶² Intriligator, Michael D. and Brito, Dagobert L., “Nuclear Proliferation and the Probability of Nuclear War,” Public Choice 37, No. 2 (1984), 247–60CrossRefGoogle Scholar; Mueller, John, Retreat From Doomsday: The Obsolescence of Major War (New York: Basic Books, 1989)Google Scholar.