Gaming North Korea’s missiles: what are the mathematics of peace?

The equilibrium of the world's different nuclear arsenals is a victory for game theory - but North Korea's ambitions could upset the balance.

By Michael Brooks

For a few decades after the Second World War, we were quietly kept safe by innovations in the field of mathematics. Those were the golden years of game theory, when dour-faced men built algorithms that were designed to ensure that no atomic bomb would be detonated in anger again. It was one of the unsung accomplishments of modern science. The period of balance between Russia’s and America’s arsenals, intentions and fears was a victory for game theory.

The creation of equations based on real-world scenarios has since scored successes beyond the realm of war avoidance. Economics, biology and materials science are just a few of the fields that have benefited. Whether you are looking at customer behaviour, responses to parasites or how metal alloys form, game theory provides a way to understand processes of compromise and co-operation. However, it may be time for theorists to turn their attention back to national security.

Those early nuclear-arms-related equations have largely remained balanced because missile defence technology has been slow to develop. This is partly a result of the difficulty of the task, but there has been no necessity, either: the current nuclear powers have learned that diplomacy can maintain an uneasy peace.

All of that changed on 7 February with North Korea’s demonstration of rocket technology, moving the regime closer to possessing an arsenal of intercontinental ballistic missiles. The immediate response from the US was that an effective missile defence system had become an urgent priority. With North Korea in the game, compromise and co-operation may no longer be possible.

But missile defence is harder than you might think. In 1967, when the then US defence secretary, Robert McNamara, first proposed a shield to nullify a Chinese missile attack, scientists, engineers and mathematicians used game theory to demonstrate its weaknesses – namely decoys. In 2011, the Pentagon issued a report confirming that the trajectory of missile defence technology had followed the scientists’ predictions.

A warhead is best intercepted in space after release from the missile. Unfortunately, at this juncture, it is easy simultaneously to release and inflate a flock of metallised balloons. No anti-nuke interceptor is able to tell the warhead from the balloons and so an interceptor is almost certain to miss its target. According to the Pentagon, pre-empting this and acting before the balloons are released “requires Herculean effort and is not realistically achievable, even under the most optimistic set of deployment, sensor capability and missile technology assumptions”.

The trouble is that military minds seldom believe in fundamental limits, even if these are put forward by scientists. Nuclear equilibrium is as much a mental as a mathematical state. The balance achieved by the present arsenals, modernisation programmes and testing schedules is a delicate one – and talk of missile defence systems has long threatened to upset that balance. If the US begins a renewed effort to create its long-sought shield, other nuclear powers – notably the Russians and the Chinese – will worry that some technological miracle could render their arsenals impotent. So, thanks to North Korea, the nuclear game has just got a lot more complicated. Ensuring that our wary stand-off continues will require a new effort in the mathematics of peace.