A nuclear three-body problem

China’s growing nuclear weapon capability risks overturning the relative stability of nuclear deterrence based on only two adversaries

Chinese author Liu Cixin’s novel The Three-Body Problem was an international best seller, and was later turned into a really interesting, though somewhat controversial Netflix TV version (for the record, I liked it). The Chinese title is 三体 or sān tǐ, which translates as just three body or bodies (san ti is also the name given to the aliens), but the English name makes explicit the link to the problem in mechanics of a system of three orbiting objects, which can become unstable and unpredictable. There is no general closed-form solution to this problem.

The theory and practice of nuclear deterrence has until now been based on a two nation model. Although other nations acquired nuclear weapons, the dominant fact of the Cold War was the nuclear standoff between the USA and USSR, both of which by the late 1960s had enormous numbers of nuclear weapons mounted on land missiles, bombers and submarines. Nuclear thinking in the West evolved through game theory, which is the theory of interdependent decision-making. A foundational text was The Theory of Games and Economic Behaviour by John von Neumann and Oskar Morgenstern, which provided a mathematical basis for relatively simple two-person, non-cooperative zero-sum games (games where there is a fixed amount of payoff, or benefit, that the players each try to get for themselves, knowing that the other person will anticipate and react to their actions). This became the basis for thinking about nuclear strategy. Once you move to non-zero sum and cooperative games, things rapidly get more complicated.

Another, perhaps more famous contributor to game theory was John Nash, whose story was told in the film A Beautiful Mind. A Nash equilibrium is a situation when two players have no rational reason to change their behaviour, conditional on what they believe about the other player, assuming they are both rational. It’s a form of equilibrium of expectations. The most famous concept of nuclear deterrence, mutually assured destruction (MAD), is a type of Nash equilibrium. It has worked so far, but note that it depends on everyone being rational, if such a dire state of affairs can be so described (*).

A less mathematical version of game theory was developed in the 1950s and 1960s, especially associated with Thomas Schelling, who much later, in 2005, won the Nobel Prize for economics. Describing Schelling as an economist doesn’t really do justice to the breadth and imagination of his writing. He, along with theorists in think tanks like the Rand Corporation (**), developed ideas that helped to understand and manage the truly globally important question of how the USA and USSR could avoid destroying not just each other, but the entire planet. His book The Strategy of Conflict is one of the most interesting I read during my graduate study years.

Some of those ideas appear perverse, such as that defence against the enemy’s incoming missiles was destabilising. If the USA could prevent the USSR from destroying it, then it could attack the Soviets with impunity. Anticipating this state of affairs, the USSR would rationally attack first, before any such defence was operational. Ideas of credible second strikes and survivable command and control arose out of a fruitful, though very fearful, interplay between theory and practice, most terrifyingly during the Cuban Missile Crisis of 1962. That crisis showed, among other things, that even though two leaders both desperately wanted to avoid war, the logic of events, combined with needing to save face, could push two nuclear powers to the brink.

As an example of misunderstandings that contributed to the crisis, Soviet leader Nikita Khrushchev regarded putting nuclear weapons on Cuba as a defensive action, because it would deter an American attack on the island nation. So he was sincere when he promised President Kennedy that he would not put offensive weapons on Cuba. But Kennedy, when he found out about the weapons from spy plane intelligence, felt he had been lied to. Weapons that could destroy Washington DC in less than 15 minutes could hardly appear defensive to him. This, and much more rich detail, is described in the recent BBC audio series and podcast The Bomb: Kennedy and Khrushchev, narrated by Nina Khrushchev, the great-granddaughter of Nikita Khrushchev, and Max Kennedy, the son of Robert F Kennedy, the Attorney General and brother of President Kennedy, who played a pivotal role in the crisis. The series includes interviews with Serhii Plokhy, author of Nuclear Folly and Sergey Radchenko, author of To Run the World: The Kremlin’s Cold War Bid for Global Power, both of which books I highly recommend.

The near-miss over Cuba led to arms control treaties between the nuclear superpowers that reduced the total number of nuclear weapons and, for a while, increased mutual trust and confidence that the nuclear threat could be managed. But the relationship deteriorated again in the 1980s, when the world twice came very close to accidental nuclear war (***).

Problematic though the situation was, it was conceptually manageable because the two nations had a broadly similar and symmetrical view of the situation. But that is no longer the world we live in.

China joins the nuclear club

China tested its own nuclear weapon in 1964 at Lop Nur in Xinjiang Autonomous Region, and a thermonuclear weapon (“hydrogen bomb”) in 1967. Chinese Communist Party Chairman Mao publicly belittled the significance of nuclear weapons, arguing that China had so many people that it would survive even a nuclear war. This sort of comment alarmed the Soviet leader Nikita Khrushchev, contributing to the ending of Soviet support for the Chinese nuclear programme, amid a wider split between the two nations. China, a very poor country at that time, achieved its own nuclear capability unaided, and without the intelligence from the Manhattan Project that the USSR had received from spies. It was also at great economic cost, during the period of slow or negative economic growth caused by the Great Leap Forward in the early 1960s. The nuclear programme was also one of the very few parts of the government that was protected during the Cultural Revolution of 1966-76.

But China never built more than a minimal deterrent, a few hundred bombs, combined with a declaration of no first use (it’s questionable whether such a statement means anything, but for what it’s worth the USA has always refused to make any such declaration). The USA and USSR, at various times both potential enemies of the People’s Republic of China, largely ignored its nuclear capabilities. In fact the USA, in its truly crazy Single Integrated Operations Plan of the early 1960s for fighting a nuclear war, made no distinction between the USSR and the PRC, planning to destroy both countries in any nuclear attack, regardless of where the threat came from (****)

But now the PRC has started adding to its nuclear weapons and modernising its delivery mechanisms. US analysts believe China is aiming for 1,000 warheads by 2030 and perhaps more after that. Alongside the wider transformation of the Chinese military, this may seem natural and reasonable and China may have good reasons for doing it. But it turns a just-about-understandable two-body problem into a three-body one. If the USA decides it must have enough weapons to match Russia and China, then it will increase its nuclear warheads (or more precisely bring into active use those already stored in its stockpiles). That risks triggering a reaction in Russia, which in turn could make China increase further its own nuclear weapons. There is no clear equilibrium in this relationship, which risks turning into a new arms race.

On top of that, other countries in Asia may conclude that the optimal strategy for them is to acquire (South Korea, Japan, Vietnam) or further increase (India, Pakistan) nuclear weapons. The more nuclear weapons and nuclear states there are, the more likelihood of accidental or deliberate nuclear war. If you want to be reminded of how bad that would be, two recent books lay out the utterly terrible consequences. In Annie Jacobson’s Nuclear War: A Scenario, the world is more or less over in just over an hour after an initial launch. Mark Lynas’s Six Minutes To Winter explains more thoroughly, and depressingly, how nuclear war causes nuclear winter and the probable deaths of most human beings. I believe that both authors wrote these books to try to wake people up to the threat we already face. The film A House of Dynamite explored convincingly (to me) the knife-edge on which nuclear decisions rest.

This topic of China’s nuclear expansion has been written about extensively in the US foreign policy world for several years, since it became clear that China is increasing its nuclear weapons. It has become particularly topical this week (5 February 2026) with the expiry of the last arms control agreement reached by the USA and USSR, though there is some small hope that the USA and Russia will continue voluntarily to stick to the warhead limits.

Unhelpfully, China has not explained its policy or how it sees the wider picture. One view is that China is itself responding to the US progress in missile defence and precision conventional strike abilities, that could neutralise China’s ability to retaliate (its “second strike” ability). Nuclear strategising can easily descend into assuming the worst about your actual or potential adversaries. This is a form of the “security dilemma” identified by so-called realist international relations thinkers, in which one country’s rational actions to defend itself trigger another country to respond, thereby confirming the first country in its actions, in a downward spiral. This spiral could become lethal (for all of us) in the nuclear case.

While nobody expects any nuclear nation to reveal its secrets, the USA and USSR, and later Russia, learned that it is in their mutual self interest to communicate, to reduce the risk of misunderstandings. The “hot line”, a direct method of communication between the US and Soviet leaders, was set up after the Cuban Missile Crisis. (Apparently the first test message sent was “The quick brown fox jumped over the lazy dog”, famously a sentence containing all 26 letters of the alphabet. The Soviets were apparently baffled about the cultural significance of foxes and dogs in the USA).

China, not having the folk memory of the Cuban Missile Crisis or those frightening moments of the 1980s Cold War, perhaps has to learn this lesson in its own near miss, but that is a very scary way of building some kind of new understanding that could manage the emerging three-body nuclear threat.

We have to hope that in this case of the three-body problem, there is a solution.

China joins the nuclear club

Further reading

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