LQ

# THE STRATEGY OF INFLICTING COSTS

## T. C. Schelling

This paper was stimulated by a remark of Frederic M. Scherer's about the notion "that a nation should weigh its own costs against the costs of its enemy" in choosing a strategy or in allocating resources to defense. He said the logic of it escaped him.

I doubted that it did, and began to develop a complacent defense of the proposition only to discover that indeed the logic--or at least an important part of the logic--had escaped me too; and where first I thought that economists like Scherer and me should neither disagree nor be in doubt about the proper formulation of so simple a principle, I no longer find the principle so simple.

Scherer argued that the proposition is valid only if the amount of resources a rival can allocate to defense is fixed--"an assumption unsupported by recent history," he says--or if an arms race is being waged as a "game of economic ruin." He doubts the advisability of the latter strategy, at least for the United States against the Soviet Union. And he goes on to criticize a good deal of recent defense analysis for its "zero-sum" orientation, its assumption

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of strictly opposing interests.*

The proposition that the enemy's costs in meeting some threat that we pose, or in responding to some measure we take, should be taken into account in deciding whether the measure is worthwhile, is not hard to defend in a zero-sum context; and one can set Scherer straight by saying that the zero-sum context is all we had in mind. Either it was made explicit, or he should have perceived that it was taken for granted. But though we can defend the letter of the proposition, it is not so easy to defend the spirit. Should we confine ourselves to the zero-sum context, where the answers are comparatively easy, evading the more interesting contexts where the answers may be harder? Should we defend the cost criterion in a way that increases our vulnerability to Scherer's charge that quantitative military analysis too readily assumes a zero-sum relation, even while our discussions of strategy are almost exclusively non-zero-sum?

We cannot justify zero-sum reasoning by assuming that the amount of resources an adversary will put into the contest is fixed. Even

*See his review of E.S. Quade, "Analysis for Military Decisions," *American Economic Review* 55 (Dec. 1965) 1191-92.

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with a fixed budget the contest will almost surely be dramatically
non-zero-sum. "Deterrence," for example, is a meaningless notion
in a zero-sum context; so is "surrender," and so are most of the
limited-war strategies discussed today; so are all the notions
suggested by terms like "accidental war," or "brinkmanship"; and of
course so are nearly all alliance relationships and arms-race
phenomena. The fact that war hurts--that not all the losses of war
are recoverable--makes war a non-zero-sum activity whether budgets
are rigidly fixed or not. To get a zero-sum contest one needs
a much more restrictive assumption than the one Scherer mentioned.
The idea that we have some interest in an adversary's domestic
economy and that that interest is not simply opposite to his
interest and measurable in the same currency as our military interests,
is only one among many reasons--and surely not the most important
reason--why military relations are non-zero-sum both in peace
and in war. Furthermore, a "game of economic ruin" is not zero-sum
if war itself is an alternative to progressive economic ruin and
if war is worse than economic ruin, or the threat of such ruin
can be used to extort concessions. In fact it is hard to see how
military relations can ever even approximate a zero-sum model
unless things have reached the point where all but two extremes
among the possible outcomes have become--for reasons of diplomacy,

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personality, technology and geography, or some profound incompatability
between the two sides--practically unattainable and irrelevant to
decision. There are, of course, tactical arenas within a non-zero-sum
relation that can be dealt with, at least in a practical sense,
as separable zero-sum local contests, but care is even needed at
the tactical level.

Separable Zero-Sum Components

There are indeed zero-sum military problems that can be
separately analyzed. Cryptography is an example: one scrambles
or enciphers tactical communications to keep secrets. The avoidance
of predictable regularities is another: one tries not to be
predictably unprepared on Sunday mornings. One randomizes the firing
of hardened missiles so that they will not be simultaneously and
predictably vulnerable during the moment the lids are off the silos
before the missiles are on their way. Search and evasion will be
randomized; depth and proximity fuses will be set on zero-sum
principles; and scarce ammunition may be allocated among sites on
strictly zero-sum criteria. These schedules and allocations
relate usually to some fixed set of resources in circumstances
where there is no thought of influencing enemy intention; and it is
no more costly to do things right than to do them wrong. Though the

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wider context may be a non-zero-sum campaign or bargaining process, it is purely a matter of local efficiency to do things right.

There is another way that a zero-sum situation can be embedded in a larger non-zero-sum context and yet be susceptible of isolated zero-sum analysis. This is if the payoffs are some kind of bargaining power, usable in some subsequent process of negotiation or coercion. A zero-sum contest can be fought to determine which side gets some advantage--some ammunition, some intelligence, some technology, or some part of the world that is significant for its later strategic role in some confrontation or bargain. It will be hard to classify such a contest as "zero-sum," though, if the two adversaries have significantly different evaluations of the subsequent bargaining process. It will also be hard to classify it zero-sum if they can anticipate the later bargaining and make later behavior conditional on the conduct of the momentary contest. But if the thing fought over is uniquely recognizable as an advantage to the side that gets it, (or advantage to either side to the extent that it shares in it), if the non-zero-sum use of the asset comes later--and particularly if there are only two outcomes: he gets it or we get it--the momentary contest can be treated as zero-sum.

There is a special case worth mentioning, though difficult to give a contemporary interpretation. That is the case in which both

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sides agree to a "trial by ordeal"--to play a game of chess for the
treasure, or to hold a tournament for a lady's favor. An agreement
may be reached to avoid a potentially destructive non-zero-sum
contest by letting some game (in the literal sense) determine the
outcome. David and Goliath fought, according to Yadin, to make
unnecessary a bloody battle between their armies; both sides agreed
(though in the end Goliath's did not keep the agreement) to let the
battle of champions determine which army would become slaves to the
other.* Arbitration has this character; a zero-sum battle of wits
determines the outcome, both sides being committed to abide by the
result to avoid the potentially more destructive bargaining that
would ensue if they were unable to wager their positions on some
conventional procedure.

Tactics: Zero or Non-Zero-Sum

It is often alleged that strategy is non-zero-sum while tactics tend to be zero-sum. There is a good deal to the notion; it often means merely a mission, once ordered to be accomplished, should be accomplished efficiently. Bombing the civilian population of Japan was not a zero-sum strategy; but once it had been decided to

*Yigael Yadin, *The Art of Warfare in Biblical Lands*, Vol. II, New York, 1963, pp. 267-269.

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light fires in Tokyo there was every reason to do it with a minimum
of risk and effort, and each individual sortie could be scheduled
from a zero-sum point of view.

On the other hand, a decision to take prisoners, to bomb civilians in order to destroy a military installation, or to suffer casualties in achieving an objective, are not zero-sum decisions. Furthermore, even though back at headquarters a particular engagement may be viewed as zero-sum, any operation carried out by live human beings is a multi-person non-zero-sum game. Maybe some kinds of combat have become so mechanized that the individual combatant's valuation of his own life has little relevance to his choice; but the history of warfare tells us that tactical engagements have always been multi-person non-zero-sum games in which fear disabled more combatants than weapons, and discipline counted: more than numbers, weapons, terrain, or technology. General Rommel's orders to his Panzer units to open fire before they were in range, because enemy soldiers ducking their heads were as good as enemy soldiers dead, was a recognition of the non-zero-sum character of local combat.

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Costs and "Sub-Optimization"

Still, the zero-sum contest is an interesting bench mark, a
limiting case worth being acquainted with, and often a decent
approximation in some localized arena of the larger contest; and
it is worth while to get the cost principles straight for that
situation, too. The principle merely says that, in taking account
of the consequences of some act or decision, any costs that the
enemy is obliged to incur have a positive value to our side, just
as the costs we incur in carrying out the act, or in consequence
of the decision, must be valued negatively. And a corollary of
this principle is that if substantial costs have to be incurred by
the enemy, and more modest costs incurred by us, and if as a result
of incurring those costs the enemy keeps us from accomplishing
anything locally, nevertheless his higher costs are a perfectly
valid objective, or motive, for our going ahead with the action;
and we can even think of the local contest as a battle of costs.

Now, if the whole situation is strictly zero-sum, and if our
analysis is intended to comprise the whole situation--if we are
engaged in what Charles Hitch has called "grand optimization"--there
is no need to bring in the concept of "cost," whether the enemy's
costs or our own. The best over-all strategy, worked out in all
its detail, is just the best strategy, all things considered; and

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any relevant costs have already been considered. The fact that a
particular measure on our part will "cost" an adversary some lives,
ammunition, fuel, manhours or anything else is of no concern if we
have made allowance in our over-all model for the withdrawal of lives,
fuel, manhours, and so forth, from their alternative uses. Costs
are intended to reflect the payoffs _left out_ of our local analysis.

It is when we engage in "sub-optimization," and the local
contest for which we are sub-optimizing uses resources that might
have been allocated instead to other arenas, or resources that can
be saved and used later in different arenas, that we need to make
specific allowance for costs. If some particular measure is under
consideration and we have allowed for all of its local tactical
consequences but find that it either uses or saves some resources on
our side, and that the adversary's accomodation increases or decreases
some inputs on his side, the local payoffs do not tell the whole
story. The extra resources are withdrawn from other fields of
battle, resources saved are available to other fields of battle;
it is all the same war and we have to take account of what happens
on those other fields. Costs are simply the measure of consequences,
or payoffs, that occur outside the boundaries of our local problem.
If there is no economic linkage between our local problem and the
rest of the whole problem--if all local resources are specific, if

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nothing can be added or withdrawn, if nothing can be saved for
later use--then the local payoffs tell the whole story, and we need
make no allowance, through "costs," for payoffs beyond our horizon.

Costs are merely a rough index of the payoffs that we are not
responsible for in our sub-optimization. Of course, if all resources
are so specific that to find out the "worth" of resources added or
withdrawn elsewhere we have to examine in detail their impact on
those other fields of battle, then we have to solve all the problems
at once in order to solve our local problem, and sub-optimization is
infeasible. Sub-optimization only works if there is little or no
connection between the local problem and the over-all problem, or
if there is some convenient approximate way of making allowance
for the impingement of the local problem on the bigger problem.
If the enemy has an actual price system that works rationally, or
if he manages nevertheless by direct means to allocate his resources
efficiently; and if the enemy's economy is characterized by
substitution possibilities, alternative mixes of inputs to produce
a given output, alternative uses of outputs, and all the other
characteristics we usually impute to a resilient and rational
economy; and particularly if the situation allows the enemy time to
adapt economically to the measures we confront him with; then we
assume that increments of enemy resources can be allowed for as

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"costs" and "savings" without regard to how the individual items
that comprise the resources are allocated elsewhere, or precisely
where they are drawn from.

That seems to be all. It could be illustrated by a set of a
dozen zero-sum matrices, each dependent on the share of total
resources allocated to it, the payoffs to each side being the sum
of the payoffs in the individual matrices, with "optimization" being
achieved only when neither side could improve its position by
reallocating resources among the different arenas. A shift in the
parameters of one matrix might open opportunities for one side to
improve its position by shifting resources into that matrix; if
they are shifted from the other 11 matrices in a way that minimizes
the reduction of payoffs in those other matrices, there is a
calculable "cost" that is of interest to both sides. This "cost"
will tend to be the same (for modest increments) whichever the
matrix is to which resources are being added, and it permits local
decisions to take account of their impact on other fields of battle.
If we combine the 12 matrices into a single game we can drop the
cost concept altogether; if instead it is convenient to analyze
the 12 different games separately, the "cost" figures serve an
essential purpose and make local optimization consistent with over-all
optimization.

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Costs can of course be used wrong, and most of the exposures
of the "fallacy" of this cost reasoning relate to some mistaken
use. I have been asked whether I would buy a $100 nylon vest
to protect myself from a 5 cent bullet, as though I should not
according to the cost criterion--the factor of 2000-to-1 against
me makes it a bad investment--yet if I treasure my life I shall
obviously buy the vest. In this example the cost criterion is
merely backwards; the relevant question is whether my adversary
should buy a bullet knowing that I can nullify his investment with
a bullet-proof vest. He has wasted his money if the vest is cheap,
made a splendid investment if my vest is expensive, and if asked
what he accomplished by buying his bullet should have the good sense
to say that he imposed a cost on me, not that he hoped to kill
me and was frustrated.

The "Exchange Rate"

We need of course some kind of "exchange rate" to tell, without
extending our analysis into grand optimization, whether a cost
imposed on the enemy is worth the cost to us of imposing it. Unless
we and our adversary have comparable economies there is no reason
why the appropriate exchange rate should equate percentages of
gross national product or any other economic magnitudes on the two

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sides. We can say, as a kind of shorthand, that a cost is worth
incurring if it imposes a "greater" cost on the other side; but then
we must mean that "costs" have been measured in the same currency
as the payoffs in those other arenas. If we calculate "costs"
for the two sides in any other way, such as money costs converted
on a foreign currency market, percentages of GNP, or what the
enemy's specific inputs would cost at our prices, there is no reason
to suppose that a straightforward comparison of "greater" and
"smaller" will tell us the story.

The Incidence of Costs on Consumers

Suppose an enemy fuel shortage falls on consumers, and the
enemy values the health and comfort of his people, deplores the
death of infants, suffers in the suffering of his people and takes
those civilian values into account in his own planning, not for the
military advantage they give him against us but just for their own
sake. Then the relation between us is non-zero-sum. We may like
his babies to be warm and healthy, prefer that they suffer, or not
give a thought to it; but we are most unlikely to be just as disposed
to welcome the suffering of his people as he is to deplore it, and
in our cost calculations we should take no credit for the prospect
that some children will be cold or sick because we damaged enemy

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fuel supplies.

In fact, the enemy may care less about his own people than we do--if by "enemy" we mean the management or directorate of the military opposition to us. Suppose the enemy neither likes nor dislikes his subjects--perhaps because he is a military occupant of another country and does not much care whether the citizenry suffers or prospers--and we do not care either, because our sole concern is military advantage. The game is still zero-sum, but if a local fuel shortage will fall on the local citizens who have less heat in their houses, or if a local fuel saving means merely that less is requisitioned locally, there is no "cost" to be allowed for in our problem. The cost is passed along to somebody outside the contest. The costs we want in our analysis are those that reflect the flow of resources among the sectors of the contest, for all the sectors comprising an integrated adversary relation between us; if other sectors are involved, and can absorb or yield resources to the sectors engaged in the contest, then either those sectors matter and the situation is non-zero-sum, or they do not matter themselves and distort the price system. We have to correct for them. That makes it harder to ascertain the costs and to use the figures properly, but does not contradict the principle.

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The Non-Zero-Sum Context

Let me turn now to the non-zero-sum adversary relation that usually characterizes war and military preparations. First let us remind ourselves of some of the reasons why wars and arms races are non-zero-sum. There is civilian damage--pain, disability, death, privation, lowered living standards, fear and anxiety, both during the war itself and after the war. There are battle casualties; soldiers are people, and when they die there is not only a loss of military assets but also human pain and grief. There is, during military buildup, some influence of that buildup on the likelihood that war will occur. Military preparations affect the character of any war that ensues, including the capabilities of both sides for keeping it limited and stopping it. Wars and military preparations affect precedents (like the use of gas or nuclear weapons) that affect the conduct of future war. The enemy in a war is often a potential ally or subject; in colonial wars, the killing of an enemy soldier is the loss of a colonial subject; and since the time of ancient Athens, economic loss inflicted on today's enemy weakened a future ally or subject. War involves hostages; much of the population of Western Europe was a potential hostage in German hands during World War II. Adversaries can gain or lose honor and prestige, in a non-zero-sum fashion. War can induce political

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change; the monarchs of 1914 destroyed most of the system they liked. War can weaken both adversaries vis-a-vis other countries. There is for some countries a moral cost in the conduct of war. War is often a multi-person relationship; the generals' plot on Hitler's life and the shift in authority within Japan after Hiroshima remind us that nations are not the same as individuals or teams of like-minded individuals. Finally there is the point mentioned by Scherer, that the military expenditure of potential adversaries can affect the civilian welfare and political conduct of the country, affecting the likelihood of war itself.

We could go on, but there is no need to. Zero-sum adversary relationships are hard to find in any important area of human affairs; and people in need of an example in a hurry sometimes point to war as one of the rare zero-sum social relationships, but this is pure thoughtlessness. About the only thing that could make war/zero-sum would be a **belief** that war were zero-sum, a belief so obstinately held that the war would indeed be conducted that way. People who put chessmen on the dust jackets of books about strategy are presumably thinking of the intellectual structure of the game, not its payoff structure; and one hopes that it is chess they do not understand, not war, in supposing that a zero-sum parlor game catches the spirit of a non-zero-sum diplomatic phenomenon.

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Elasticities of Demand: A Comparative-Advantage Example

Because Scherer and others have already pointed out that costs imposed on the enemy may be passed along to his population, so that we gain less than we hoped or even lose if we prefer his civilians not to bear the cost, let me suppose a fixed enemy military budget and explore some of the ways the cost criterion gets complicated as we acknowledge that our interests and our opponent's are not strictly opposed. Consider him to have a given budget that he can allocate among two or three or even more kinds of military resources for the event of a war with us. And consider how our deployment of forces affects his deployment, and in what ways our choices can influence his choices and how we should evaluate his choices.

To begin, consider a simple model. He has a budget with which to buy missiles and sites. If he spends it mostly on missiles and concentrates on a small number of sites, he gets more missiles than if he went to the added expense of dispersing his missiles among a larger number of sites. With dispersion he has more real estate to buy, more facilities to install, more roads, communications' equipment and security personnel, and possibly more active and passive defenses to procure with his limited budget.

At the same time, his missiles are more vulnerable if they are

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concentrated; and for "second-strike" purposes he prefers a more
dispersed force. His value system, we may suppose, contains
two variables: the number of missiles that he can buy (with which
he could launch an attack) and the number of missiles he could
expect to have left over in case we attacked him. We can call these,
if we wish, his "first-strike" force and his "second-strike" force.
They are of course the same force, but they are evaluated differently
according to who starts the war. A large vulnerable force has a
comparative advantage towards striking first; a smaller less
vulnerable force has a comparative advantage toward striking back.

How he disperses his missile force--how he uses money that might
have been spent on missiles to buy more sites--will depend, among
other things, on how expensive the sites are. If sites are cheap
he will buy a site for each missile (perhaps more, if we cannot
tell empty sites from those that have missiles, and must target
as many sites as he buys). If sites are expensive he cannot much
disperse his force without greatly reducing its size; beyond some
point, even for a second-strike force, more dispersal becomes
uneconomical.

To be simple and explicit, suppose that his costs are merely
a linear function of missiles and sites; missiles are procured at a
constant price, sites are procured at a constant price, so that his

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"transformation curve" denoting combinations of missiles and sites is a straight line. We have a given force with which we can attack all of his sites; and, not knowing the particular distribution of missiles among those sites, we would distribute our attacking missiles evenly if in fact we attacked. Suppose our attacking missiles have independent probabilities of kill, so that the survival of a site is merely the survival probability in the face of one attacking missile, compounded by the number of missiles fired at the site. Let X denote the number of missiles he buys, Y the number of sites, and M the size of our attacking force, with P the survival probability of an individual site under attack by a single missile, K his total budget (measured in units equal to the price of a missile), and a the price ratio of sites to missiles. The expected number of missiles surviving our attack would be equal to:

$$M/Y$$
$$XP$$

Substituting the budget equation, this gives:

$$\frac{M}{Y}$$
$$[K - aY]P$$

If he wants to maximize the expected value of his second-strike force, he merely maximizes that expression with respect to Y. If he

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wants to maximize some function of second-strike forces, giving positive value to his first-strike force, we have to specify the function but then we can go ahead and solve his problem.

Now let me pose this question. Suppose we have a new weapon, perhaps a new ingredient in the warhead of our attacking missiles, that if unanticipated by the enemy would increase the potency of each of our missiles against any site it is aimed at. It makes more vulnerable all of his sites, hence his entire missile force. Never mind what it actually is; just imagine that it is available to us at modest cost. Suppose the enemy knows about it and can either see that we have it or assume that we have it. And suppose that this particular capability is one that is readily countered, at a price. The enemy can defend against this measure with complete effectiveness but has to spend money to do so. Do we hope his countermeasure is cheap or expensive?

Now, the distinguishing characteristic of this particular measure is that it attacks sites, not missiles. Of course, if it destroys a site it destroys the missiles on the site; that is the whole idea. The point is this: the enemy's countermeasure

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is associated with his sites, not with his missiles, so that the
aggregate cost of defending his force depends on how many sites
he has to protect, not on how many missiles he has to protect.

His countermeasure, we suppose, is adding smoke screens, anti-aircraft batteries, police dogs, duplicate generators, or some other active or passive defense to individual sites in such a way that the cost does not depend on how many missiles are on the site.

The point of this distinction, of course, is that it affects
his allocation of resources between missiles and sites. That is,
it affects the allocation of his budget between first-and-second-strike
forces. And we _care_. Furthermore, we care _in a way that is not_
>_strictly opposed to the way he cares._ He may, for example, be
mainly concerned to deter us with the best second-strike force
he can buy and have little interest in either attacking us with
his whole force or threatening to attack with his whole force.
(He could even prefer to reduce our apprehension, and attach
negative value to his first-strike force.)

And we might prefer that he buy a second-strike rather than a
first-strike force, that is, a force whose second-strike capability
is relatively larger and whose first-strike capability is relatively
smaller. We may not; it depends on whether we want to deter him
or to attack him, and it depends on what we think raises and

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lowers the likelihood of our having to attack him or his having
to attack us. But if we mainly want something like "stable
deterrence" our preferences may somewhat coincide with his: he
wants a good second-strike force _even_ at the expense of his
first-strike force, we are willing to see him get a good second-strike
force _if_ it is at the expense of his first-strike force.

Now, do we want the price of his sites, as distinct from the
price of his missiles, to be high or low? If we can raise the price
of those sites by threatening them with a measure against which
a costly countermeasure is available, do we want to make the threat?
Do we like the countermeasure to be expensive or inexpensive? And
would we prefer to threaten him with a measure whose defense is
associated with his missiles rather than his sites, so that they
raise his cost per missile rather than his cost per site?

We can solve the problem explicitly and find out--at least we can
if we specify his preference-function as among first and second-strike
forces, and our preference function as between his first and
second-strike forces. But off-hand about the only conclusion we
can jump to is that we would rather raise the price of his missiles
than the price of his sites (if the aggregate costs in both cases
are of about the same magnitude) because we anticipate that he will
use more of the cheaper of the two inputs, and we know which one it
is that we want him to use. Intuition, analogy, or quick mental

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arithmetic will not give us that answer about site costs. If some
neutral country sells the site-defense countermeasure and we can
influence its price policy, we do not yet know whether we want
it cheap or expensive.

The key to our decision is what, in the familiar language of
economics, we can call the enemy's "elasticity of demand"
for missile sites. Whatever he spends on sites is unavailable
to spend on missiles. If we want to minimize his first strike force,
we want to minimize the money he spends on missiles, therefore
to maximize the money he spends on sites. Will he spend more money
on sites, or less, if the price of sites goes up? Is his demand for
sites inelastic or elastic? We have to work the problem to find
out.

In the specific form in which I set up the problem above, if
the enemy's exclusive interest is a second-strike force, it turns
out that his demand for sites is slightly inelastic. He spends
somewhat more on sites if the price of sites goes up, less on
missiles. To put it differently, the "income effect" of the price
rise outweighs the "substitution effect" and, though missiles have

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become cheaper relative to sites, he now buys fewer missiles.

In this particular problem the answer is independent of
the initial costs of sites and missiles and independent of the
budget; but this is a special case and we might have to give a
more qualified answer if we worked with a more complicated
model--if for example, missiles or sites were bought along
rising or falling supply curves, if sites supported or
interfered with each other or if missiles did, or if the
enemy's preference function were slightly different. It is
easy to make a minor change in this model and reach the
contrary conclusion--that we do not want sites to become
more expensive to the enemy, we want the countermeasure
sold cheaply, and we should avoid confronting the enemy
with our own measure in the first place if we can, to
keep him from finding missiles more attractive, relative
to sites, than they used to be.

This kind of consideration cannot arise in the
zero-sum confrontation. It furthermore can arise, as it
did here, without regard to whether we want the enemy's
people to be better housed

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and fed. It can arise without our putting a positive value on
his second-strike force; it requires only that our preferences not
be strictly opposed to those of the enemy, that is, that our
"trade-off" and his not be identical, or, in economic jargon, that
our indifference curve not be tangent to his at the point where his
is tangent to his budget line.

Elasticities of Demand: A Jointly Valued Capability

Consider another case, where the answer should no longer
surprise us after working through the first case. Let there be
some military capability that the enemy wants and that we want
him to have. This is something we want him to buy not just
because it uses resources that he would otherwise spend on things
that we deplore even more; this is something it is positively
in our interest that he have. We want him to have it even if it
is free of charge, and we might even provide it if he could
not buy it himself. It might be a device to avoid nuclear accidents,
to minimize the false alarms that might cause him to launch war
itself, to reduce nuclear fallout, to facilitate armistice,
to permit the recovery of dead or wounded from
the battlefield, to care for

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prisoners of war, to avoid the military destruction of fish and
wildlife, or anything else. The point is, he wants it and we want
him to have it; we have no military interest in denying it to
him, and if it gives him any sort of local advantage in a zero-sum
contest somewhere, that disadvantage to us is outweighed by its
beneficial effects over all.

Suppose, now, there is some measure available to us with which
we can destroy it. Or suppose we can affect the price he pays for
it, causing it to be more expensive or less expensive. What should
we do?

There is a lot to be said for being nice about it, if only to
dramatize the common interest, to set a precedent for preserving
assets of value to both sides, to induce him to avoid taking
reciprocal measures that would hurt us as well as himself, and for
other essentially diplomatic or bargaining reasons. Leaving
those aside--just considering our influence on his allocation of
resources--we have two interests here. First, we want him to
possess that capability; even if we threaten to destroy it, we
want him to take steps to defend it. Second, we want to divert
resources from other capabilities that we do not like into this
capability that we do like, not just because we like this capability
but because we like it to draw resources from the rest of his budget.

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Again it is the elasticity of demand that matters. If we
know that he will defend that capability at all costs, because
it is important to him as well as to us, then we can safely threaten
it, forcing him to defend it, knowing that the net effect will be
fewer resources available to the part of his force that we do
his warning
not like. We threaten--to pick an extreme example--to spoof/system
so that he would launch a successful first-strike against us--a
first-strike that, though successful, he would rather not launch and
would launch only in the mistaken belief that he was under attack.
He anticipates our spoofing and spends money to tranquilize
his warning system, to make sure that we cannot provoke him into
an attack that he would prefer not to launch, to make sure that we
do not bring down on ourselves a war that we deplore as much as he
does. We watch him cut back his ground forces, or his first-strike
capability against our strategic forces, or his second-strike
capability against our civilian assets, or some other program that
opposes our interests, in order to maintain the capability that,
though we like it too, he likes very much.

But be careful. If we put the price so high that he prefers
it
to do without it--if we threaten/in a way that costs him too much
to defend it--we divert no resources from other parts of his budget,
we merely prevent his having something that we both badly want him
something
to have. Or if the countermeasure is/ that he can buy in varying

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quantities or degrees, raising the price or supply curve may cause
him to buy less of it. If his demand is actually elastic, he ends
up with less of what we want him to have, more of what we do not
want him to have, and we lose on both counts. If his demand is
inelastic he ends up with somewhat less of what we want him to have,
less also of what we do not want him to have, and we have to weigh
the one against the other. If the elasticity is not uniform,
we have to watch out that we do not push the price or the supply
curve upward beyond the point where his cutback of other forces
ceases to outweigh his cutback of what we like him to have.

The point of this example is two-fold. First: to emphasize
that there **are** military capabilities that we want the enemy
to have--not just that we dislike less than we dislike other
capabilities, considering his marginal rate of substitution, but
that we attach positive value to, want him to have, and would even
buy for him if he did not procure **for himself**. Second: that
just as we might want to **lower** the price of a force that we prefer
him **not** to have, to induce him to draw resources from other parts
of his budget that we like even less, we could want to **raise** the
price of things we prefer that he have, for the same reason. Here
it is a case of wanting the income effect on the rest of his budget
to outweigh the substitution effect for this particular item.

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Elasticities of Demand: A Diversionary Threat

Next consider the enemy's response to a new capability on our side to inflict damage on his civilians and their property. And suppose, just to clarify the principle, that what we threaten to destroy is of negligible military value, unavailable to his military economy. This could be because he cannot mobilize these civilian resources before or during the war, or because they have low military value (a strong comparative advantage toward civilian value). Pain and life itself would have this quality, as would potential members of the labor force too young to work until the war is over; so would physical assets that would be more important after the war than during the war, and structures too specific in their civilian use to be transferable directly or indirectly into military strength. The idea is simply that, whatever the value of threatening such destruction, we get no military advantage from carrying out the destruction; nor does the enemy suffer a significant military disadvantage. It is pure civilian loss, a kind of "side payment" that he makes but we don't get.

Aside from revenge, justice, and other moral and psychological satisfactions that might be provided by such a capability--and recognizing that these satisfactions could be drastically negative--there appear to be two main purposes served by such a

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military threat directed against enemy civilian value. Both depend on _influencing_ his behavior. One is _deterrence_ (i.e. bargaining advantage) and the other is _diversion_ (of resources from other uses). "Deterrence" implies that he refrains from some action as part of a bargain, according to which we carry out the destruction or not according to whether he refrains or not. This could mean that he refrains from starting a war, refrains from opposing us if we start a war, refrains from inflicting damage on us in the course of a war, or even refrains from continuing a war that he has already started. (We could go further, and actively demand some positive performance on his part--submission, evacuation, reparations, or some other concession. In this case the broader term, "coercion," would be more suitable.)

"Diversion" implies that he anticipates our attack on his civilian value and does something to mitigate the effect. We may or may not want him to divert resources; but if we do, it constitutes a kind of coercion--a threat that we will destroy civilian value unless he diverts resources to protect them. To the extent that he can attenuate our threat by shifting resources, he merely holds us to our bargain by carrying out his part.

Now, how do we feel about the costs to the enemy of countering our threat in some fashion? This will depend on how he counters

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it, and at the expense of what other capability. Two important
possibilities are that he defends his civilian assets and that he
procures a force of his own with which to threaten ours. If he
defends his people, it could be at the expense of his battlefield
forces--that is, the forces he could field in a "zero-sum contest"
for territory or booty--or it could be at the expense of the force
with which he threatens our civilian assets. (It could also be
at the expense of some measures, of the kind suggested earlier, to
which we attach positive value.) The diversion might also change
the character of the forces he threatens us with, such as their first
or second-strike advantage, and change his expectation of the
likelihood of war.

There are two important limiting cases to consider. First,
that the damage we threaten would _surely_ deter the enemy in all
circumstances, so that we need no longer worry about how he allocates
his military resources (and, if he could acknowledge the adequacy
of our deterrence, he might as well disband his force). Second,
that though the damage we could do would severely reduce the net
gain to the enemy from any war he might contemplate, it would
certainly _not_ deter him if on other grounds he had decided to have
his war. Between these two limiting cases are high and low
probabilities of deterrence with their complementary probabilities
that war will occur.

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If he is surely deterred, we have no interest in diversion.
Our only interest is that diversion be incapable of spoiling our
deterrence. We want the costs of an adequate defense to be
prohibitively high. We might be indifferent to whether he simply
sat deterred, or shifted all of his military resources into civilian
defense and had nothing left to oppose us with; but if we are
absolutely sure of deterrence we can lose interest in the shape of
his military force.

If deterrence is clearly inadequate, our only interest is
diversion. We want him to withdraw as much as possible from his
other military capabilities as the price of defending himself against
our threat--at least, we do unless he withdraws resources from
some capabilities that we prefer him to have. Assuming that he
withdraws his resources from the battlefield, or from a first-strike
strategic force or from a second-strike force that does not shift
in character toward a first-strike force under the pressure of a
smaller budget, we want the price of defense to be low enough to
be attractive, high enough to be costly. Again, "elasticity of
demand" is the pertinent analogy, although we are likely to be
less interested in the "price" of a "unit of defense" than with
the whole curve relating damage to investment in defense. If
defense is too costly--if it is too ineffective compared with its
cost--the enemy will not invest in it. We get nothing for our

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trouble. In fact, anticipating that he will not defend his civilian assets, we should not procure the threatening force in the first place. (Paradoxically, the enemy in this case prefers that his civilian assets be indefensible in the face of a threat not large enough to deter him; the indefensibility of his cities makes our threat purposeless, and we will not bother to buy the threat.)

He may instead react by developing a reciprocal civil-damage force of his own. If he does, we probably want it to be expensive, both to take resources away from other arenas and to minimize the potency of his own threat. We may not like this response, even if it is costly, and prefer not to provoke it. From his point of view, if he can afford either to defend his cities or to threaten ours but cannot afford both, defending and threatening may be equally attractive. From our point of view they are not equally attractive.

These considerations are important. Burton Klein pointed out in his study of German war economics that one of the main consequences of strategic bombing of Germany in World War II was the sizeable diversion of German resources into air defense--up to one third of all German military production went into active defense against air attack at the climax of the war.* If the

*Burton H. Klein, *Germany's Economic Preparations for War* Cambridge, 1959, pp. 232-33.

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purpose was merely to defend military strength, it was part of a
zero-sum contest not related to what I have been discussing. But
if the object was to preserve Germany and Germans, not just war
potential, it was the diversionary principle expressed above. At
the present time the United States has to decide whether it wants
the Soviet Union to invest, or not to invest, in ballistic missile
defenses. We presumably do not want such defenses to be so
effective and so cheap as to spoil our threat altogether; we might
prefer a large Soviet investment in city defenses that, though
inadequate to spoil deterrence altogether, would appear a useful
hedge against the likelihood of war to the Soviet leaders *yet would*
*take* large resources away from their strategic offensive forces or from
their battlefield forces. What we want the Soviets to do about
ballistic missile defenses is a complicated question, but it is an
important one and not answered by zero-sum analysis.

Between the two extremes of sure deterrence and no deterrence
at all, the deterrent and diversionary motives can both be present.
We can hope that our threat provokes enough expenditure on the
defense of civilian assets so that if war occurs the diversion will
have been significant, without the defense being so effective that
it greatly reduces our deterrence. How to weigh these two
considerations depends on our notion of what it takes to reduce

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greatly the likelihood that the enemy is deterred. We probably
have to pay something in deterrence to achieve the diversion,
because the enemy will not waste money on a futile defense; still,
he could find it worthwhile to spend money to reduce damage in a
possible war, without the extent of such reduction necessarily
affecting his willingness to launch war or to provoke it. If we
get to draw the enemy's "supply curve" of defense--the relation of
damage-reduction to money spent on it--we want to be very careful
how we draw it. Anybody who then shifts it upward may do us as
much harm as if he shifted it downward.

Adaptation and Costs

In zero-sum situations, the enemy's adaptation to some new
initiative on our part always reduces the value of that initiative.
We see an opportunity or a new capability, take advantage of it, and
get a certain score at his expense if he does not adapt to the
change in our posture; his adaptation takes away some of our
advantage. The net advantage to us depends on how costly his
adaptation is; but in zero-sum situations, we'd always prefer that
he be unadapted, that he not know of our new initiative, or find
adaptation too costly, or be institutionally unable to adapt.
In non-zero-sum situations we can prefer that he adapt, and he can
prefer to adapt, knowing that we prefer it too.

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In fact, we can undertake moves that make no sense, have no value for us, unless he does adapt. The diversionary principle just discussed is one of these. Facing an enemy threat to our civilian values, we might be attracted to a completely defensive posture that virtually nullifies his threat. We might alternatively be attracted to a completely offensive posture because it obliges him to dismantle his offensive posture and devote all of his resources to defense.

Thus it is perfectly possible that our preferred posture in the face of an enemy offense is pure defense, but we like even better a pure enemy defense that is induced by a purely offensive posture on our side, and that we choose the offensive posture accordingly. If he does not adapt as we hope, we end up with offensive postures on both sides; that could be our last choice. In this case, unless he adapts as we expect, improving our position as he rectifies his own, our move is a bad one, for us and perhaps for him.

## Adaptive Cost-Avoidance: Comparative Advantage Again

Consider one more case, just to sharpen up the contrast between zero-sum and non-zero-sum calculations. The enemy is building up a force, or is about to buy a force, of 100 "semi-hardened" missiles at a cost of $1 apiece. Our attack force can inflict 50% attrition on his 100 missiles if we attack. He