Stability of Nuclear Forces
This application will help you explore the stability of nuclear forces in the
presence of MIRV (Multiple-Independenlty-Retargetable Vehicles). A missle may
have one or more warheads. More warheads per missle leads to cheaper forces, but
also fewer targets for the enemy, since your warheads are concentrated on fewer
Note that probabilities smaller than 0.001 are shown as 0.0.
This was originally an applet, but security concerns caused me to remove the applet. I've updated the code and changed it to an application. You can download both the source and an executable jar file below.
Two opponents each have some number of missles. Each of the missles has some number
of warheads. The warheads all target the missles of the other side.
When one side has a high probability of being able to destroy all
of the missles of the other side, the situation is said to be unstable.
This is true for two reasons.
- The side with the "first strike capability" might be tempted to strike
first in a tense situation, knowing that they had a high probability of destroying
the forces of the other side.
- More subtle, though, is the thinking of the weaker side. Knowing that the
stronger side will be tempted to strike first, and knowing that the weaker
side's force will likely be destroyed if that happens, the weaker side has
an even stronger incentive to strike first, knowing that they have no way
to strike second. This leads to the instability.
Therefore it can be bad for the stronger side to be too strong in some situations.
Being too strong can actually decrease your own security.
Henry Kissenger has admitted after the fact that it was probably a mistake
to "MIRV" the US misssles during the cold war as it led to such an instability.
You may change any of the figures in the boxes that now have values (
Missles, Warheads per Missle, Kill Probability per Warhead, and Stability Threshold).
When you are done, click on the Calculate button The other boxes
will be updated. The situation is Stable if neither force can destroy the others
forces completely with a probablility higher than the threshold.
Questions for Study
- Does increasing your number of missles tend to increase or decrease stability?
- Does putting more warheads on each missle tend to increase or decrease
- Does putting more warheads on each missle, while decreasing the number
of missles to keep the number of warheads constant tend to increase or decrease
- Does increasing the accuracy of your warheads tend to increase or decrease
- Historically, what was the situation at the end of the cold war. Determine
the number of missles and warheads per missle of the US and Soviet forces.
Was the situation stable or unstable? Suppose the same number of missles had
only one warhead each?
This is based on the probability of independent events.
If the probability that one warhead can kill its target is .90 then the probability
that it will not is 1 - .90 = .10.
If we send 3 warheads against the same target and none interfere with the
others, then the probability that they all miss is
(.10 * .10 * .10) = .001.
Therefore the probability that the target will be destroyed is 1-.001 = .999.
If we have 4 such targets, then the probability that all four will be destroyed
if we send 3 warheads against each of them (requiring 12 warheads) is
(.999 * .999 * .999 * .999) = .996
However, if there were 1000 such targets, then the probability that we would
destroy them all with three warheads each would be
(.999 ^ 1000) = .368.
where ^ is the exponentiation operator.
The first strike capability is computed from the formula
( 1 - ( ( 1 - killProbability) ^ warheadsPerTarget) ) ^ numberOfTargets
This work was done jointly by Detrich Fischer of Pace
University who developed the model, and Joseph Bergin of Pace
University who programmed it. This version was built using Visual Café
for the Macintosh from Symantec. An earlier version was done in Hypercard.
July 29, 2015