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War Without Pain, and Other Models

  • Thomas C. Schelling (a1)


I don't know how many economists, teaching business fluctuations or the corn-hog cycle, have devoted an hour to the household thermostat; I know several. Cybernetics, I am told, drew attention to similarities between vacuum tubes and animal nerve cells, and made predictions about the human nervous system that were verified by surgery. An article on feedback related artillery fire-control and automatic oil-pipeline systems to the ecological complementarity of the lynx and the rabbit. Economists compare the closeness of election campaigns to the market forces that make two brands of cider taste much alike. Analysts of rumor, best sellers, and epidemic diseases have been led independently to the equation for the logistic curve; and the collapse of Batista has been compared to the collapse of a stock market. Individuals with conflicting internal values have been likened to a two-person committee with a complicated voting system; and recently the paradigm of the “prisoners' dilemma” has been used to characterize preemptive attack, cheating on a test ban, and Rousseau's illustration (five men cooperating in a stag hunt when one spies a hare) of the value of enforceable contract.



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1 New York 1950.

2 Simon, H. A., “A Formal Theory of Interaction in Social Groups,” American Sociological Review, XVII (April 1952), 202–11.

3 The most pertinent part of Richardson's work can be found in Richardson, Lewis F., Arms and Insecurity (Pittsburgh and Chicago, 1960), edited by Nicolas Rashevsky and Ernesto Trucco. See especially Chapters 2–5. For a review, see Harsanyi, John C., “Mathematical Models for the Genesis of War,” World Politics, XIV (July 1962), 687–99.

4 Shubik, Martin, Strategy and Market Structure (New York 1959).

5 Rapoport, Anatol, Fights, Games, and Debates (Ann Arbor, Mich., 1960). For a review, see Aumann, Robert J., “The Game of Politics,” World Politics, XIV (July 1962), 675–86.

6 Newman, James R., The World of Mathematics (New York 1956), II, 1238–53.

7 Quoted in the biographical note to Richardson, Lewis F., Statistics of Deadly Quarrels (Pittsburgh 1960), xxvi.

8 Huntington, Samuel P., “Arms Races: Prerequisites and Results,” in Friedrich, Carl J. and Harris, Seymour E., eds., Public Policy (Cambridge, Mass., 1958), 4186.

9 Burns, Arthur Lee, “A Graphical Approach to Some Problems of the Arms Race,” Journal of Conflict Resolution, III (December 1959), 326–42. Some interesting unpublished work has been done by Michael D. Intrilligater of the Massachusetts Institute of Technology.

10 Valavanis, Stefan, “The Resolution of Conflict when Utilities Interact,” Journal of Conflict Resolution, II (June 1958), 156–69.

11 Princeton 1960.

12 The presentation of his model reflects this concept of “mood.” Richardson begins, and Rapoport follows him, with a mathematical description of how mood changes as a function of the mood of the adversary—a pair of differential equations. From this can be derived the curve relating one side's eventual mood to the mood of the other side—what Boulding calls a “partial equilibrium curve.” To Richardson the instantaneous reaction is the fundamental process; the derived equilibrium curves are an analytical construct. (“The equations are merely a description of what people would do if they did not stop to think.”—Arms and Insecurity, 12.) In Boulding the method is reversed. Boulding conceives of each nation's having a preferred position on its own arms buildup scale for any given position the other country may be in. From this he can derive the adjustment process (Richardson's differential equations). Analytically, the one can be translated into the other; but the starting point depends on whether the process is regarded as one of conscious goal-seeking or of instantaneous reaction. This difference in conception is reflected in the organization of Rapoport's book; his theoretical arms race is analyzed in Part I, “The Blindness of the Mass,” rather than in Part II, “The Logic of Strategy.” He puts the arms race in what he calls “social physics,” and relates it to psychological epidemics and other phenomena of mass reaction like the lynx-rabbit cycle. Boulding's explicit references to Shubik make clear that Boulding, perhaps because he is an economist where Rapoport is a mathematical biologist, prefers to deal with self-conscious organizations as decision units. He also, as an economist, sees quantitative limits on arms programs; in Richardson's model there is no boundary to the process except war itself.

13 Drawing a diagram with two axes, one labeled “us” and the other “them,” leaving it to the reader to interpret the behavior as tangible or intangible, may be momentarily useful for articulating some concepts of interaction. It is a fault of Boulding's presentation that he switches back and forth between a military-program interpretation and a friendliness-hostility interpretation, as though the two were the same. He also seems to imply—and die need for simplification provides some excuse—mat the mood of a nation can be analyzed as diough it were the mood of an individual. There is undoubtedly some useful analogy between one nation's “hostility” toward another and one person's “hostility” toward anodier, and there may even be some structural similarities; but they are not the same phenomenon. Also, from a methodological standpoint, one has to distinguish between quantitative phenomena that show continuity over time—going from less to more by traversing values in between—and mose diat can jump discontinuously from large to small or from love to hate.

14 Kent, Glenn A., “On the Interaction of Opposing Forces Under Possible Arms Agreements,” Occasional Paper No. 5 (Center for International Affairs, Harvard University, 1963).

15 Huntington, , “Arms Races,” in Friedrich and Harris, eds., 64.

16 International Committee of the Red Cross, Draft Rules for the Limitation of the Dangers Incurred by the Civilian Population in Time of War (2nd edn., Geneva 1958), 144, 151.

17 Incidentally, if distance is measured directly in units of transport cost, not in miles, the loss-of-strength gradient is replaced by an equivalent parameter of “distance,” and we have essentially the model used by Wright, Quincy in Appendix XXIX to his Study of War (Chicago 1942), 11, 1389–91. In Wright's model a country can be conditionally viable in relation to a single enemy while the latter is deterred by the presence of a third country, in a balance of multinational power. A two-country model can probably not explain how the Americans managed to emerge independent from the Revolutionary War.

18 Clausewitz emphasized the danger of offensive overextension; an offensive that loses momentum in enemy territory leads not to an equilibrium frontier but to a reversal. (Trench warfare as in World War I was not anticipated.) Boulding might allow for this, but not adequately unless he explicitly includes uncertainty. There is no uncertainty in his model; to include it would change the character of the model, especially in relation to the role of threats. Boulding's model cannot handle the preemptive aspect of the Franco-Prussian War or the German gamble on quick victory against France in 1914.

19 Hoag, , “On Stability in Deterrent Races,” World Politics, XIII (July 1961), 505–27.

20 Western Europe from the Thirty Years’ War to World War I, less the Napoleonic period. See Fuller, J. F. C., The Conduct of War: 1789–1961 (New Brunswick, N.J., 1961), especially Chapters 1, 2, 5, and 6.

21 Even for combatant troops there may be a non sequitur in the St. Petersburg Declaration. After stating that the only legitimate object in war is “to weaken the military forces of the enemy,” it goes on to say that “for this purpose it is sufficient to disable the greatest possible number of men,” and that this object would be exceeded by arms that aggravate the sufferings of disabled men or render their death inevitable Similarly, the IVth Hague Convention (1907) forbids “arms, projectiles, or material calculated to cause unnecessary suffering.” (Explosive or poisoned rifle bullets, for example, were outlawed.) I believe it is a fair observation, both from the history of warfare and from the history of tactical doctrine, tbat one main way to weaken the military force of the enemy—often more important than killing and wounding—has been to make the individual enemy soldier too scared to fight effectively. Ardant du Picq's Battle Studies, for example, is mainly preoccupied with how to get soldiers to move forward and use their rifles rather than drop behind the nearest hummock; Frederick the Great, as well as the Romans, recommended sharp steel behind the advancing troops to help offset the sharp steel in front of them. Whatever the merits of banning them, the weapons of battlefield horror—fire, war cries, elephants, or bombs with sirens—have usually had that same “legitimate” purpose: “to weaken the military forces of the enemy.” Terror is not a weapon to which only civilians are vulnerable.

22 Fuller quotes from a letter by General Sherman after he took Atlanta: “If the people raise a howl against my barbarity and my cruelty, I will answer mat war is war.…If they want peace, they and their relatives must stop the war.” (Ibid., 108–9.)

23 Boulding also avers, in the language of cybernetics, that command and control are necessarily diminished by the modern weapons. “The longer the range of the projectile, the more difficult the receptor-control problem becomes; it becomes more difficult, that is, to know whemer the projectile has reached its intended mark and correspondingly more difficult to aim it with a high probability of reaching the mark” (p. 267). Before we become too bemused by sheer mileage, I suggest we ponder some pre-nuclear instances of the fog of war. “During the decisive days of the Marne, the German headquarters at Spa had almost entirely lost touch with meir units, could get no word from them, and could send only fragmentary instructions. The order to retreat was given by a Lt. Colonel of the General Staff who had been given full powers by General Headquarters and sent to the front to see what was going on.” Ferrero, Guglielmo, Peace and War (London 1933), 17. The episode is described in some detail in Churchill, Winston S., The World Crisis, 1911–1918 (abridged and rev. edn., London 1943), 176–81.

24 Shubik's firms are interested in profit, not maximization of gross sales or the absorption of rivals for its own sake. If Boulding had made payoffs or indifference curves as explicit in his war model as in his arms-race model, he might have been led to the analysis of deterrence, intimidation, limited war, and surrender. Firms, of course, are not single-minded rational calculators, nor are nations at war; what we get is still only an abstract, incomplete model. But the same is true of Boulding's “active-defense” model.

25 At the Battle of St. Jacob-en-Birs in 1444 the Swiss, outnumbered fifteen to one, attacked the Dauphin's invading army and piled up twice their number in enemy corpses before being themselves extinguished. The price too high, the Dauphin retired with his troops. “From that day the Confederates were able to reckon their reputation for obstinate and invincible courage as one of the chief causes which gave them political importance.…It was no light matter to engage with an enemy who would not retire before any superiority in numbers, who was always ready for the fight, who would neither give nor take quarter.” (Oman, C. W. C., The Art of War in the Middle Ages, Ithaca, N.Y., 1953, 96.) Five hundred years later the Finns demonstrated that the principle still works.

26 A strategic reason why conquerors have often been assimilated by the conquered may be that, to enjoy their conquest, they must cease being unencumbered marauders and settle down in wealth and vulnerability. Viking ships of male warriors could surprise the scattered farmers, commandeer their animals for greater mobility on land, and be gone before a superior force could be concentrated against them. But “the settlement of the invaders in the Danelaw…greatly simplified the military problem of the English. An enemy with towns to be burned and fields to be ravaged was much more vulnerable than one whose base of operations was the open sea.” (Ibid., 25.) The Vikings were nowhere easy to pacify, but they appear to have become most peaceable where they had immobile possessions, like homes and families.

27 In a recent paper, Boulding looks at the threat as an abstract human relationship and epitomizes it by the proposition, “You do something nice to me or I will do something nasty to you.” (Boulding, “Toward a Pure Theory of Threat Systems,” to appear in Papers and Proceedings, American Economic Review, 1963.) This, in my scheme, is a “compellent” rather than a “deterrent” threat. It does sound a little antagonistic.

War Without Pain, and Other Models

  • Thomas C. Schelling (a1)


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