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War and Zero-Sum Games

ISSUE:  Winter 1977

One of the most deeply ingrained prejudices in America’s perception of the world is the belief that war and international conflict in general can best be defined, and are most clearly understood, in the image of a game; specifically, in the image of an athletic contest. Wars, for Americans, are events which are won or lost, in the same way that a game is won or lost, that is, adversary encounters with unequivocal rules and clearly defined goals; and the winning or losing of a war depends upon the achievement of certifiable, quantifiable results, in the same way that scanning a score determines who is the winner or loser of an athletic encounter. This prejudice is deeply buried in the consciousness of Americans, whose life is dominated by competitive values, a metaphoric imagery of athletic contests, a culture of games, which comprise such a large part of our daily experience.

Such an image is profoundly misleading and lies at the heart of serious misconceptions and distortions in our perception of war and international affairs. This image, for instance, effectively prevented us from developing a realistic view of the Vietnam War and gave plausibility to a “hawk” definition of that conflict which failed, precisely because it was based on a false analogy between wars and games.

The frustrations of the Vietnam War stemmed from the fact that by all “scoring” rules, Vietnam was a “victory” for the American military: body counts, kill ratios, bombs dropped, equipment destroyed, territory captured, all the well-known numerical counters by which military victory is traditionally defined. But this military “victory,” somehow, could not be translated into changes in the larger world which were considered advantageous to American interests. Barry Goldwater’s repeated criticism of a political leadership which did not know how to “win” the war, or General Westmoreland’s carping attempt to demonstrate that he did not “lose” the war, continue to strike a responsive chord in an American public which has become disenchanted with Vietnam, but which remains conditioned to the view that war is a game, and is unable to comprehend how we failed to “win” that particular contest.


War, however, is not a game. A game is an artificial, cultural creation in which purely arbitrary, man-made rules are imposed on a segment of human experience. A game is explained, its purpose defined, by those objective circumstances, those rules, which determine winning or losing. Winning or losing, in a game, brooks no argument, for its rules describe, with great precision, the circumstances which constitute winning or losing by definition. A game is defined by a voluntary consensus established by the players, not only that they will play according to the rules but that these rules will satisfy the definition of winning or losing. Thus the result of the game is purely objective; it is not affected by the subjective attitudes of the players. What defines a game of tennis is that when the score stands 6—2 against me, I have lost the set, by definition, regardless of subjective factors, regardless of my conviction that I have not “really” lost. My prior acceptance of this definition, my voluntary acceptance of these “rules” create a game. The violent confrontation we call war is in no way dependent on this kind of consensus. It is, in fact, the absence of such a consensus which defines a war, and this occurs when societies enter into conflict situations of such intensity that they can no longer play games with each other.

War cannot be evaluated by the scoring techniques used in a game because war, unlike a game, is not a self-contained event. A game is an end in itself, unlike a war, which is always fought for another purpose than the fighting itself. War is an instrument for the realization of other ends, ends which exist beyond and outside the context of the war. It is true that games can also be used for “other” ends, that people play games to maintain physical fitness, sharpen their wits, quicken their reflexes, enjoy a “good time”; games can be viewed not simply as ends in themselves but as means to other ends, related to the larger experience of life. Still, before they exist on this instrumental level, games qua games can, and indeed must, exist as ends in themselves, as self-contained events, evaluated in terms of their own rules. Winning in a football game is defined as scoring more points than the opposition, not by the lessons in sportsmanship the players may have learned through the game or by the opportunities the game afforded for the physical conditioning of the players. Regardless of what other purpose may have entered into the decision of the players to participate in a game, it is possible to separate these other purposes from the artificial limits of the game and to define a winner and a loser, wholly within the circumscribed boundaries of the game situation. The rules of a game are objective because they are self-contained and unaffected by the larger social reality in which the game is embedded.

War, on the other hand has no boundaries, no artificial restraints which define its limits. There are no rules in war; not in the sense that belligerents act without restraint, or violate some code of “fair play,” but in the sense that winning or losing cannot be determined by definition, cannot be certified by arbitration. In war, there is no agreed upon “scoring,” and winning or losing cannot be determined with precision. In fact, as we will demonstrate later, winning or losing in war cannot be determined by purely objective criteria but depends, ultimately, on subjective factors.

* These circumstances are usually given an absolutely unequivocal measure through the device of numerical scoring; although the basic function of rules remains the same in games such as chess which do not depend on a numerical scoring system. In fact, one might argue that winning, in a game like chess, is defined as the scoring of a single point; the scoring of that point depends on achieving a set of objectively defined circumstances, the mating of the opponent’s king, which play the same function, in explaining the game of chess, as the circumstances which define the scoring of a six-point touchdown in a football game.


It was the unwillingness, or inability, to define the instrumentality of the war, the attempt to view the winning or losing of the Vietnam War not in terms of ulterior goals but within the objective circumstances of the war itself, to find a “game” definition of victory which characterized the hawk supporters of the Vietnam War and which explains the conceptual weakness of their definition of that conflict. The common denominator of so much of the popular support for the war was that the hawks never asked, in fact did not want to know, what the war was being fought for.What so many Americans wanted was to “win” the war, for its own sake, as a self-contained game, unrelated to any goals.

All of the hawk critics of our Vietnam policy shared Douglas MacArthur’s conviction that in war there is no substitute for victory. The problem, of course, is how to define victory. The fatal weakness of the hawks was not that they sought victory instead of defeat, but that their definition of victory was wholly inadequate. It was, in fact, devoid of content. The supporters of the war attempted to define “winning” by a numerical assessment of the instruments of war themselves, unrelated to any goals for which these instruments might be used; they attempted to impose a “scoring” system on the war that would enable them to achieve victory objectively, “by definition.”

But what is the definition of “winning” in a war? Does it mean killing X number of people, achieving a kill ratio of X proportions, conquering X amount of territory, destroying X amount of materials? There is no way of placing a specific value on X.All the “scoring” we achieved in Vietnam failed to win the war because the outcome of the war could not be quantified and evaluated by such scoring devices, not even the brutal quantification attempted by the American general who remarked: “The French did not kill enough. If you kill enough you win the war.” But do you? Unless one assumes that the goal of the war is defined by all this killing. But not even the most bloodthirsty commander would define the goal of the war as killing Vietnamese people; that was merely a means to victory. But that victory had to be defined in terms of a goal, and the appropriateness of the means evaluated, not against some artificial numerical yardstick but by their success or lack of success in approximating that goal. Killing large numbers of Vietnamese might have brought us closer to our goal or it might not. If, having killed so many Vietnamese, the new objective circumstances created by all that killing did not represent a desired result, did not bring us closer to our defined goals, in what sense was all this killing a “victory?” In Vietnam, it was the hawk definition of such strategists as Westmoreland and Goldwater and its echoes among the uninformed American public that produced a no-win policy in the strictest definition of that much abused phrase. For our political leaders, as guilty as they were of dishonesty, stupidity, arrogance, and insensitivity, did have some notion, no matter how confused, of ultimate, political goals which they sought to attain through the instrument of war. One might argue the inadequacy or immorality of these goals. But they were goals. By defining victory in unreal, “game” terms, unrelated to any concept of what we might be doing in Vietnam, the hawks divorced the war from any recognizable purpose and thereby made winning literally impossible. As a result, they transformed the war into a meaningless and ugly “killing game,” in which we were driven to an insane and purposeless escalation of destruction. The admonition to kill as many Vietnamese as possible, the suggestion that we bomb Vietnam back to the Stone Age, were reflections of an inability to think through the most elementary questions about the possible advantages we might be seeking through the war and a monumental intellectual bankruptcy concerning our understanding of the structure of international politics.


This argument has brought us to what may appear as no more than a well worn truism: that war is an instrument of policy which cannot be evaluated or understood in isolation from its political purpose. Yet we have generally failed to pursue the implications of this connection to its full logical conclusion. Even as we recognize the invalidity and simplistic nature of the hawk model of war, our concepts of international conflict continue to be guided by a confusing and inadequate model based on a misleading analogy with games. For most of us continue to assume that, although war must be related to ultimate political goals, there exists a purely military dimension to war which can be evaluated in its own terms through the same self-contained “objective” techniques which apply to games. But the point is not simply to relate military “victory” to political purposes; the point is that the concept of “victory” itself is meaningless if it is divorced from the total context of the political, in fact, the human, environment of which war is a part. If we recognize that war is part of the totality of social experience, then we are driven to the conclusion that winning and losing, in war, can have no definite, objective content and must be defined, ultimately, by the application of subjective criteria, by a normative act of judgment. For all we can say about military violence is that it has produced such and such results in the world of objective reality. Whether these results comprise “victory” requires an act of judgment, of evaluation, which goes beyond any purely “objective” scoring system, no matter how sophisticated. It requires a judgment of what are, ultimately, subjective factors. They are subjective in the sense, first of all, that if war is an attempt to bring about change by violent compulsion, then the results of war are affected by the subjective responses of the players. In a war, the players are under no constraint to accept defeat “by definition,” and a player on the “losing” side of a 6—2 score may, to borrow Clausewitz’s phrase, pursue the conflict “by other means.” He may, for instance, leap over the net and attack his opponent with his racket.

The refusal of the Vietnamese to accept defeat “by definition” was, in fact, the source of so much frustration for the supporters of the war. The stated purpose of our leadership, presumably, was to “punish” the Vietnamese so severely that they would agree to the conditions we sought to impose on Vietnam. But obviously, the success of that “punishment” could not be measured by the number of Vietnamese we killed. It could only be measured by the subjective response of the Vietnamese themselves. If the Vietnamese refused to respond in the way we wanted them to respond, there was no way in which we could transcend this subjective factor by compiling “objective,” numerical assessments of our military activities which “proved” that our punishment was successful. We could not achieve victory “by definition,” since the purpose of the war, in one sense, was to compel the Vietnamese to accept our definition of victory. Whether the Vietnamese could be compelled to do so was, ultimately, a psychological, subjective question to which there could be no precise, military, “objective” answer.

In war, goals are not only incapable of the objectivity and quantification possible in games, not only incapable of the precise evaluation produced by a system of “scoring,” but these goals are constantly being altered, shifted, redefined, by the circumstances of the war itself. Because war, to the extent that it is a competitive encounter akin to a game, is one which by its very actions alters the “game” environment in such a way that, in the well-worn cliché’, one side may “win” all the battles, yet “lose” the war. In games, there can be no “Pyrrhic” victories, for in a game, the objective circumstances which define the game are unaffected by the play itself.

The possibility of a “Pyrrhic” victory suggests more than the fact that some “wins” may be too costly. It suggests that the playing of the game of war so affects objective conditions, and thereby the ultimate goals of the war, that the definition of victory is altered by the war process itself. It is as if a football team, in the process of scoring a touchdown, so altered the contours and make-up of the ball, the field, the equipment, that the very rules of the game itself were changed. As a result, the touchdown, in the new circumstances created by the very scoring of it, might now have a different “scoring” value or might even be evaluated as a “loss” rather than a “gain.”

This open-ended character of war is one reason why an objective definition of victory is extremely difficult. The action of war is so destructive that it alters the human environment in drastic ways and even consumes its very goals. In the act of attaining the objective circumstances which have been defined as victory, the violent process of war creates new, unexpected, unforeseen circumstances in which the original goals either lose their meaning or are transcended. This openended character of war partly explains the shifting ways in which the U.S.government defined its goals in Vietnam. Granted that much of the public rhetoric about Vietnam was either nonsensical propaganda or outright lying, one main reason why the U.S.government was tempted to lie so much about the war was because our military actions in Southeast Asia were altering the contours of objective reality in such ways as to undermine not only our rhetoric but also whatever real, objective factors underlay these rhetorical flourishes. The government began to lie on a large scale when the process of the war itself began to destroy all rational objectives for which the war might have been fought.

Our tendency to view war as a game, therefore, is more than a matter of cultural conditioning; it reflects a profound failure of political realism. The image of war as a game appeals to all of us because it so greatly simplifies the complexities of the international environment and provides the comforting illusion that international conflict can be understood and evaluated in precise, numerical, objective terms. The image of war as a game appeals precisely because of its simplicity, its predictability, and its insulation from real human experience. We are all conditioned to view international conflict as a zero-sum game because such an image has an appealing simplicity which seems to provide a completely reliable way of defining international affairs. It is one amenable to the kind of quantification so fashionable among Americans today, from the most simple-minded “man in the street” to the most sophisticated “behaviorists,” who believe that a conclusion becomes “scientific” if it is stated in numerical terms.

The game image of war also has appeals on yet other levels. For example, the numerical scoring systems we chose in Vietnam were guaranteed to produce American “victories,” The scoring counters we used were always in categories where we had well-known capacities to produce large numerical results: kill ratios, body counts, property destroyed, bombs dropped. We had an enormous and continuously demonstrated capacity for achieving high rates of destruction, It became appealing to define these high “scores” of destruction as “victory,” Further, the achievement of these numerical “scores” became extremely important to our collective ego as well as to the ego of our military commanders, as is clearly illustrated by General Westmoreland’s recent apology for his role in the Vietnam War. His criticism of our “no-win” policy and his obsessive insistence that we did not “lose” the war underscore Westmoreland’s real concern, which is to preserve his image as a “winner.” Nowhere in his bombastic defense of his “won-lost” record is there any serious treatment of the political dimensions of the war or even any awareness that the war had any purpose beyond providing him the psychological satisfaction of being a “winner.”


War is a form of competition, a violent confrontation which would seem to lend itself to clear, objective concepts of winning and losing. Upon closer examination, however, it turns out to be extremely difficult, if not impossible, to find a plausible objective definition of victory in war. More accurately, war is an attempt to force an adversary, zero-sum game model on the reality of international relations, The decision to wage war assumes that the most effective way to change the international environment is through that violent confrontation which produces “winners” and “losers.” War is the instrument of a policy which defines international relations as a zero-sum game in which my “advantages” are gained at the expense of your “disadvantages”; my “gains” are your “losses” in a competitive scoring system. The problem is that there appears to be no way of measuring with objective certainty these “gains” and “losses.” Neither war nor international conflict can be viewed as zero-sum games, for such games require an objective, numerical quantification of human experience which does not appear possible. And although modern nations in warfare have killed large numbers of people, destroyed large amounts of property, and organized impressive movements of armed forces over large areas of territory, there is no clear evidence that all this destructive activity has resulted in “gains” for any of the warring parties.

What was gained by Israel in “defeating” the Arab nations in the Six Days War except a state of enormous military danger which threatens the very existence of Israel? What was gained by Germany from 1938 to 1940 in “winning” Austria, Czechoslovakia, Poland, in “defeating” France except its own destruction in the holocaust of World War II? What did the United States gain by “winning” the nuclear arms race between 1945 and 1963 except to create an international environment in which the United States faces the daily threat of its own extinction? One could multiply the examples of military conflict in history where an honest examination would raise serious doubts concerning the advantages attained by the so-called “winners” of these violent confrontations.

War, historically, appears to be one of the least successful ways of promoting national interests, and the inefficacy of war increases in direct proportion to its increasing destructiveness. In fact, the successful use of power might be defined as one in which the confrontation of “winning” and “losing” is avoided. For “winning” always carries a psychological cost which not only makes it extremely difficult to persuade “losers” to accept defeat but also creates circumstances which tend to checkmate the successful use of power.

Partly because of these destructive costs, war, in the 20th century does not seem capable of producing even predictable results; and the most obvious character of war, at least since 1914, has been that it has resulted in almost wholly unforeseen consequences. Moreover, the emphasis on military violence and the search for “winners” obscure other, more vital factors in the process of historical change. Could not one plausibly argue, for instance, that the most significant “gains” Europe derived from the Crusades were associated not with the violence of the armed knights but with the activities of those Italian merchants who infiltrated the Muslim Near East? And was that infiltration any more than marginally related to all the violent activity of such personages as Godfrey of Bouillon or Richard the Lion Hearted, historical figures with infinitely greater romantic glamour but whose feats of arms were perhaps of little consequence?

It may be that the issue of war has been posed in false terms. Although violence and that organized violence we call war have accompanied the entire record of human history, that historical record does not offer very convincing proof that war, at least in modern times, can produce the victories it claims to achieve. The real question is not whether war is immoral but whether it makes any sense. And the fact that modern nations periodically engage in orgies of destruction may be proof not that war is a necessary instrument of international politics but rather a form of periodic madness unrelated to a rational definition of national interest.


The phenomenon of war, however, is not accidental, and we are deceiving ourselves if we dismiss war as simply an aberration. War is the logical extension of a view of international relations, based on the analogy of games, which views international relations as a zero-sum game producing “winners” and “losers.” The increasing incidence of war, and its increasing destructiveness, are both logical expressions of this model. If wars are viewed as competitive encounters which must be “won,” the competing states must seek comparative military advantages against one another.

The increasing sterility of war as an instrument of policy, its increasing inability to achieve desired results, to produce “winners,” may reflect the inadequacy of this view of the world. Perhaps we could obtain a clearer understanding of war, and of international relations in general, by relating them, not to the narrowly restricted, contrived, and artificial experience of a game, but to the total complexity of human experience. To what extent is a game a fit model for understanding that experience? In what sense is a man’s experience, a man’s life, a success? Such a concept, ultimately, must be defined subjectively, through normative criteria.

An individual may set himself very clear, well defined, objective goals; and if the attainment of these goals entails competition against other individuals, he may characterize the attainment of the goals as “winning,” But such a conclusion is a subjective, normative judgment, concerning the desirability, not only of the goals themselves but of the fact that their attainment depends on denying them to others, to those who are the losers in this competition. A definition of winning depends, not on the fact that life is, objectively speaking, a competitive game, but on a normative judgment concerning the desirability of goals obtained through competitive games playing.

We are constantly confronted with evidence which suggests that this experience of “winning” does not necessarily bring satisfaction to people. It is this perceived dissatisfaction with the competitive aspects of our society that leads us to conclude that people value certain goals, certain conditions, in their existence, which seem unrelated to a game definition of winning. The inadequacy of the concept of “winning” is perhaps even more obvious in the area of international relations. There the gap between the claims of “victory” and the actual, felt experiences, the welfare and happiness of the people whose nation claims “victory,” is even more glaring.

President Kennedy, for instance, defined our attempt to make a manned landing on the moon as a competitive “race” with the Soviet Union; so that when we did land men on the moon, in 1969, we had “won” that game. But that victory, like any game encounter, was a purely contrived event. It was a victory by definition, by the arbitrary definition of President Kennedy, of what he defined as “good” for America. In fact, one could plausibly argue that the moon program had cost the American people large sums of money which they could have used more profitably to increase their welfare and economic security. In other words, the American government had defined as a “win” the attainment of certain circumstances which were not necessarily beneficial to the American people or which people in America might not judge to be beneficial to themselves.

Ultimately, all judgments of foreign policy, of the international behavior of one’s own nation, rest on purely subjective factors, on a purely personal evaluation. There can be no “victory” in war, in international affairs divorced from such subjective considerations. We all have, and must have, our own, personal definition of the national interest, and we may not all agree, for instance, that what’s good for General Motors is good for America. The definition each of us makes of our national interest cannot be contained in an “objective” scoring system. There is no way in which we can define a series of circumstances in the international environment which are objectively, that is, unrelated to subjective judgments, to the advantage of the American nation. There are no objectively determined goals for American policy the attainment of which can automatically be considered as “victories.” The belief, for instance, that the United States is engaged in a competitive encounter with the Soviet Union, or with the rest of the world, and that our foreign policy goals should consist of “winning,” of being “number one,” rests on normative judgments about the nature of our national interest, hence, about the nature and quality of our nation itself.


Any attempt to evaluate our foreign policy rests on subjective judgments concerning the desirability of those conditions which we define as the goals of our foreign policy. Is the history of the United States a success story? To answer that question, one must make a value judgment concerning the quality of the United States as an organized society. One must make judgments concerning such things as the happiness, well-being, freedom, economic security available to the American people in their society. The history of the United States is a success story to the extent that it approximates whatever ideals we may posit as the goals of American society or whatever conditions in American society we take pride in, that is, define as desirable for the American people.

Undoubtedly, that type of organized violence we call war has punctuated the history of the United States. To what degree have these violent confrontations brought us closer to, or further away from, the goals which comprise what we define as a good society? Only in the light of such a definition can these violent episodes be viewed as having been “won” or “lost.”

No matter how successful our destructive capabilities in these wars, no matter how much property we destroyed, or how many bombs we dropped, no matter how many people we killed, even if we killed enough to satisfy that bloodthirsty American general, these wars were not “won” if they did not bring us closer to our goals of a good American society; worse, if they moved us farther away from these goals. In no sense could such wars be considered “won” if, after all that violence, the well-being, the freedom, the happiness of the American people were significantly reduced. The winning or losing of any of these wars would have to be measured not by their destructive consequences to other people, not by a standard of military “victory” but by a standard of what was good for America unless one made a value judgment that the goals of American society should consist in the ability to kill large numbers of people. Unless one defined a good American society as one which has the ability to produce large amounts of destruction. One wonders if even these mindless audiences who responded with such childish enthusiasm to Nixon’s assertions that we were “number one” would really accept this “Nazi” definition of national success.

The inadequacy of trying to measure the success of American history by the boast that we have never “lost” a war lies not only in the infantile definition of success implied by such a boast but also in the fact that whatever qualities of goodness exist in America, whatever aspects of American life make of American history a success story, whatever there is about America which we enjoy, as people, existentially, these aspects of America’s greatness may be no more than marginally related to the vicissitudes of our military adventures. In fact, not only would it be extremely difficult to measure what our military activities have contributed to those positive aspects of American society which we define as good, but one could argue that the quality of the American experience has tended to deteriorate in direct proportion to our ability to establish ourselves as “number one” in the world.

It is admittedly difficult to break the bonds of cultural conditioning, and we have all been so conditioned to the notion that wars are “won” and “lost,” that international conflict is a competitive, zero-sum game, that the argument contained in this essay may appear willfully perverse or absurdly idealistic. Yet an honest look at the history of international conflict in modern times must raise serious doubts concerning the unquestioned assumptions we make about “winning” and “losing” in international competition.

Given the extremely dangerous state of international relations, given the supreme threat of nuclear holocaust, it becomes urgently necessary for us to make the effort to rethink these automatic clichés, and the purpose of this essay will have been served if it does no more than cause us to re-examine critically some apparently hackneyed assumptions.


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