CND estimate that the cost of Trident Replacement, Britain’s nuclear deterrence, will peak at £205 billion. It’s likely to be more. The military sector, a barren landscape for showcasing cost efficiency, is notorious for destroying budgets. However, despite possibly higher expenditure extravagance, the public has remained largely unfazed. It was only the perceived threat of Jeremy Corbyn that provoked any strong reaction. When asked during a BBC interview whether he would ever press the nuclear button as PM, he raised voter heckles by replying “no, 187 countries don’t feel the need to have a nuclear weapon to protect their security, why should those five need it themselves?”. During one leader debate, an audience member spat at him “I find it incredibly concerning that you wouldn’t ever commit to doing that. It’s our safety that you have to look out for first and foremost”. Another opined “would you allow North Korea or some idiot in Iran to bomb us and then say ‘ooh, we’d better start talking’? You would be too late”. The Government also took umbrage, as summed up by Johnny Mercer’s response: “If Jeremy Corbyn is unable to make crucial decisions to keep our country safe, he is not fit to be Prime Minister”. On the face of it, this sounds Baldrick-level in its ‘I have a cunning plan’ mutterings. If you use a nuclear deterrence, then it has already proved not to be a deterrent. However, Corbyn is undoubtedly sailing in choppy waters, as summed up by Admiral Lord West’s appreciation of the importance of adopting a credible strategy: “When someone says ‘I’ll never press the button’ he doesn’t understand deterrence. That worries me”.
Analysis into nuclear deterrence is ultimately a celebration of Game Theory. There is some irony in that, given its earlier practical application in seeking out more effective bombing. Merrill Flood, posed with informing the US bombing campaign in World War 2, applied von Neumann’s methods into poker bluffing to direct the bombers: given the enemy will anticipate which are the most strategically important targets and increase anti-aircraft defence, how can you devise a bombing strategy that would meet military needs while avoiding too many bomber losses? Von Neumann also provided strategic advice on the use of the atomic bomb and, amongst others, recommended the bombing of Hiroshima. The switch to a deterrence perspective, however, rests with MAD. 
Mutually Assured Destruction is summed up in our first simple game. If Blue launches, Red will retaliate; both countries are destroyed. If Red launches, Blue will retaliate; both countries are again destroyed. The rational outcome is to avoid direct confrontation, perhaps offering an understanding over why difficult USSR-USA relations never did degenerate to World War 3. Corbyn is therefore being irrational as he doesn’t know how deterrence operates and how nuclear weapons saves lives. But is it really that straightforward?
First, let’s visit the history books. The USSR did have a Doomsday Machine. Named Perimeter, and discussed here, it suggests a slightly different strategy: “They built a system to deter themselves. By guaranteeing that Moscow could hit back, Perimeter was actually designed to keep an overeager Soviet military or civilian leader from launching prematurely during a crisis”. Perimeter was a means “to cool down all these hotheads and extremists”; it was a means to avoid the messiness of human emotions. Bounded rationality isn’t necessarily too convenient for the MAD gamesters.
Second, is the deterrence outcome in MAD really that stable? What happens if, say, Blue acquires a first strike capability? Perhaps a Star Wars system provides an ultimate defence and it can launch without any fear of retaliatory bombs ruining the local atmosphere? 
The result is unappealing. Blue, if Red doesn’t immediately capitulate and leave the game, should indeed launch. We shift from a realm of nuclear deterrence to one of nuclear incentive.
Third, what do revelations from recent developments in nuclear weapon policy reveal? The US has looked at fine-tuning its nuclear arsenal, providing an ‘escalation ladder’ and shifting away from the MAD binary deterrence. The thinking goes like this. Suppose Russia attacks and uses low yield nuclear weapons to annex Ukraine? The US is placed in an unwinnable position. Any response which leads to full blown nuclear war would be irrational. It faces a ‘suicide or surrender’ dilemma and Russian aggression could go unanswered. It is only with their own arsenal of ‘small’ bombs that they can consider a more calibrated response, allowing a return to the comfort of successful deterrence. But does this open a can of worms? Suppose we have a game where Blue has nuclear weapons and Red does not. Assuming resource competition, Blue will have an incentive to attack. That incentive only disappears if both are nuclear powers. Any Blue attack will generate an unpalatable situation: the MADness of full-scale thermonuclear war or, following a Red nuclear strike, a Blue retreat with heavy losses. We have developed a model advising nuclear proliferation. Those 187 countries mentioned by Corbyn all should have nuclear weapons.
The overall lesson? There is no straightforward application of Game Theory here. But how should we respond to someone using it to give a simple perspective over deterrence and a willingness to launch nuclear weapons? Perhaps first ask them why they don’t know the history, the theory or acknowledge the apparent rationality of nuclear proliferation?