-37-

could alternatively buy hardened missiles, fully invulnerable,
for $2.20 apiece. His goal is a force out of which 50 missiles
could survive attack; and at these prices, he gets it for $100
with the more vulnerable missiles while it would cost $110 if he
bought 50 of the more expensive invulnerable variety. Suddenly we
semi-
discover a device that increases the vulnerability of the hardened
type of missile; with this device, even though it costs us something
and reduces the size of our attack force, the enemy's 100-missile
force would be 75% vulnerable and only 25 missiles would survive.
What do we get for our money?

If he fails to adapt--if the device is our secret--we get a
reduction by half of his surviving force in the event we attack.
If he adapts by increasing his force of vulnerable missiles, we
oblige him to buy twice as many (to reach an expectation of 50
surviving) and raise his costs by $100, the resources coming out of
somewhere. But he has another option: he can switch to the different
type of missile and get a potential force of 50 surviving our attack
for a cost of $110. For the sake of the example, suppose that his
procurement is not too far along to permit the switch; perhaps the
one type of missile is converted into the other by additional
expenditure on the missile's environment of $1.20 per missile.

He switches, gets an estimated 50 surviving attack at a cost of
$2.20 each, spending a total of $110, or $10 more than he originally

-38-

planned. What did we get for our money--the money we spent on the device that caused him to switch his missile-procurement plan?

Mainly we got a qualitative change in his force--that is, a quantitative change along two dimensions--together with a modest drain on his military resources elsewhere. He would have had a second-strike force of 50 and a first-strike force of 100; now, faced by our new device, he procures instead a second-strike force of 50 and a first-strike force of 50. Besides costing him $10 we have cut his first-strike force by 50.

And we may like it. Unless we were planning to enlarge our own force, to cut his expected residual to below 50, and were prepared to outspend him in the attempt as he bought more missiles of his own, we almost surely like the result. We may like it quite out of proportion to the $10 extra cost we inflicted on him.

In fact, our device might have cost us so much that inflicting an extra cost of $10 would have been a poor bargain; but by cutting his first-strike force in half without firing a shot we may have achieved something well worth the cost. Maybe not; probably so; and surely the possibility has to be granted. (This case could probably be translated into the missiles-sites model of the first example above.)

His cost increase can be a gross understatement of what we gained by imposing on him the *incentive* to incur the cost. We

-39-

tilted his price comparison and were the beneficiaries of his shift
in procurement. (In the same way we might have sold him, or
given him, something that would have reduced the cost of the more
expensive missile, and been the chief beneficiary of his savings.
In fact, we could have subsidized, with cash, his procurement of
the more expensive missile, and come out ahead.) It might not
work; he might badly want a first-strike force and not shift his
procurement, or not shift it enough to make us happy. But if he
is predominantly interested in the deterrence he gets with a
second-strike force and we are substantially interested in his
not having a first-strike force, there is a bargain here. If
we draw his indifference curves between the two commodities,
first-strike and second-strike force, and ours, we may find ours
far from tangent to his; in principle they could very nearly
coincide. They need not, but they could. In this case our gain
in indeed of the same algebraic sign as his cost, but bears no
particular proportion to it. We could have had the same result if
the hardened missile cost $2.01 or $3.99, except for the net cost
to his other programs. This net cost is really separable from the
reduction in first-strike force and has to be evaluated altogether
separately. At $3.99 we are more likely to enjoy the result (unless
the resources come out of that fail-safe system we were concerned
about earlier), at $2.01 we are somewhat less enthusiastic; but the

-40-

drain on his resources is separable from the shift in
first-second-strike composition.

Notice this, too. Had he been able to buy an even "softer"
missile that was already 75% vulnerable and unaffected by our new
offensive device, but that cost, say, $0.55 and was not competitive
with the semi-hardened, our new capability would make the semi-hardened
a poor buy and his response might be to procure 200 of the soft
ones for $110. This we do not like; his first strike force is
doubled at a net cost of $10 and, though he may not much care,
we do. If both the "hard" and "soft" alternatives are available,
minor shifts in the ratio of cost to survivability can make, from
our point of view, major changes in his force: at $0.53 per soft
missile, with hard ones at $2.20, he buys 200 soft ones for $106
while at $0.57 per soft missile he buys 50 hard ones for $110. To
him, if second-strike ability is what he wants, the decision is
marginal; to us it is systemic.

I am not now trying to illustrate, once again, that we may
like or dislike what our initiative made him do, but that *minor*
variations in his relative costs can make *major* differences in our
evaluation of his response. And a consequence of this is that
***no*** single measure of his cost--whether discounted, augmented, or
changed in sign from the original estimate to make it a better
measure of what we gain--can be used as a "correction" to his costs to

-41-

reach their net worth to us. It is not just that the gain or loss
to us is poorly measured by the cost inflicted on the opponent and
needs to be corrected; it is that the gain or loss to us depends on
the *particular* way that he reacts in a particular case, to the
particular incidence of the new costs within his budget, on the
particular price comparisons that determine his response. Two
measures that identically raise *his* costs can induce changes in
*our* payoffs that bear no relation to each other. No "exchange-rate"
correction will take care of this. In the zero-sum case his
marginal decisions are marginal to us, and we can use a single measure
of "costs" to avoid tracing the ramifications of his response. In
the non-zero-sum case there is no short cut; the ramifications
have to be traced.

Conclusion about Enemy Costs

What conclusion do we reach about the role of inflicted enemy
costs in evaluating our own alternatives?

The main conclusion is that costs, in a non-zero-sum context,
do *not* reflect the changes in payoffs outside the arena of our
sub-optimization. The reason is simple: the costs we inflict, or
threaten to inflict, on the enemy can *at most* reflect the changes
in *his* payoffs outside the local arena. They do not reflect the
relevant changes in *our* payoffs because there is not the convenient

-42-

perfect negative correlation between his losses and our gains
once we drop the zero-sum restriction, that is, once we try to
extend our analysis into the (almost universal) non-zero-sum
contexts.

In the zero-sum case *his costs* reflect the *gains to us* that
our local analysis would otherwise have left out of account. In
the non-zero-sum case neither the magnitude of his costs, nor even
the algebraic sign, reliably suggests the pertinent changes in our
payoffs. Our gains may be greater than his costs suggest, less
than his costs suggest, or opposite in sign to what his costs
suggest, and will differ according to the particular choice we
pose for him.

And as mentioned above, our attitude toward his *adapting* to
our own behavior is different; instead of reducing our advantage
it can raise it or offset it in a manner not communicated by his
costs. As a corollary, our attitude toward secrecy and information
can be dramatically different from what it is in the zero-sum
case, as Martin McGuire has recently emphasized.* Taking first
move and letting the adversary adapt is never the right choice in

*Secrecy and the Arms Race* (Cambridge, 1965), especially Chapter 7, pp. 212-32.

-43-

a zero-sum game; it often is in the non-zero-sum situation.

All of our discussions of strategy emphasize these points. Our quantitative analysis should probably take them into account too. Nothing I've said--none of my examples--contains anything unfamiliar. But these familiar principles of strategy may be overdue for inclusion in quantitative analysis; or, if I'm behind the times (and Scherer is too), what is overdue is merely acknowledging that the role of costs in a careful analysis is not quite what we have sometimes said it is.

This strikes a blow at "sub-optimization," of course. What makes partial analysis valid is often the dependability of enemy costs as a short cut to all the ramifications outside the local contest. When costs are recognized as undependable--when they are no index to magnitude or even sign, neither an upper nor a lower limit, to the effect on us of the adversary's adaptation, to what happens outside our local field of vision--we have to extend our field of vision.