game theory reveals the complexities (and fragility) of a nuclear deterrent

Since the cold war, deterrence has been a fundamental principle underpinning peace between global superpowers. The idea is that if two sides have nuclear weapons, the consequences of actually using them mean the button never gets pressed.

But the strategy goes beyond the countries which own the weapons. In practice, for instance, most of Europe relies on the US for a nuclear “umbrella” of deterrence. And any country with nuclear weapons can offer guarantees of peace to others.

This is what happened in 1994 when Russia, the UK and the US signed the Budapest memorandum^[1] in which Ukraine renounced its nuclear weapons from the Soviet era in exchange for a promise to^[2] “respect the independence and sovereignty and the existing borders of Ukraine”. This was widely seen as a good idea^[3] for Ukraine and the world, reducing the risk of a nuclear accident.

But that memorandum has not served Ukraine well. As North Korea, India, Pakistan or Israel know, owning nuclear weapons – even against international agreements – ensures your protection. A piece of paper does not.

And now, across the world, the ability to offer the equivalent of a Budapest memorandum to other countries has vanished. A key part of the theory behind a successful nuclear deterrent has fallen away.

This is described in game theory – the mathematical study of strategic interactions – as the idea of a “credible commitment”^[4]. To deter a military invasion, the country offering protection must be ready to do something that hurts its own interests if it happens.

In the case of Ukraine, this has so far involved allies sending costly military equipment, financial support and enduring the small risk of further escalation of the conflict. Being a trustworthy guarantor is a matter of international reputation^[5]: a country that delivers is considered credible. But no one will trust a guarantor that breaks its promises.

Read more: Ukraine war: what is the Budapest Memorandum and why has Russia's invasion torn it up?^[6]

And while credible retaliation is important, so too is avoiding escalation. For it is also in everyone’s interest to reduce the probability of a catastrophic outcome.

Over the years, the small number of countries with internationally accepted nuclear arsenals^[7] (the US, UK, France, Russia and China) have developed nuclear doctrines. These are sophisticated and often deliberately opaque^[8] rules for escalation and deescalation.

The Nobel prize-winning economist, Thomas Schelling, argues that the uncertainty around these rules is what makes them so effective^[9]. It strengthens a system in which protection can be offered to other countries in exchange for them not developing their own nuclear capabilities.

War games

Game theory research has also shed light on the complexity of these rules^[10] of engagement (or non-engagement), such as the expectation (and necessity) of credible retaliation against an attack.

Imagine, for example, that China launches a nuclear bomb that completely destroys Manchester. A rational British prime minister may prefer to end hostilities and accept the destruction of a major city rather than retaliate and risk the total destruction of human life.

But for the deterrent to actually work, they must retaliate – or expect to see Birmingham and London disappear.

Another difficulty comes in finding the appropriate response to varying levels of provocation. When Russian-affiliated soldiers were found guilty^[11] by Dutch courts of downing a Malaysian Airlines civilian flight with 298 people onboard, including 196 Dutch nationals,^[12] there was no talk of proportional retaliation. No one seriously contemplated shooting down a Russian plane or bombing a small Russian city.

Nor was there any retaliation to Russian interventions in European elections^[13], or to the sabotage of infrastructure in Baltic states,^[14] or to murders^[15] and attempted murders^[16] on European soil.

And after the full-scale invasion of Ukraine^[17] in February 2022, the reaction of the west was consistent with principles designed to avoid escalation. Sanctions were imposed on Russia, military aid was sent to Ukraine.

But to abandon Ukraine^[18] now, forcing it to cede territory after three years of fighting, death, and destruction, would be a significant shift. It would represent a clear and deliberate abandonment of the international guarantees Ukraine thought it had.

Arsenals and agreements

Game theory also suggests^[19] that the most likely consequence of abandoning those commitments is that no country will repeat Ukraine’s mistake of giving up its nuclear capabilities. And no country will want to place their trust in potentially unreliable^[20] allies.

Europe for instance, will aim to develop^[21] its own nuclear umbrella, potentially combining French and British capabilities. It will also hasten to integrate the next likely targets of Moscow’s military ambitions.

This will include the parts of Ukraine not annexed by Russia, but also Georgia, already invaded by Russia in 2008^[22], and Moldova, partly occupied by Russia^[23].

The second consequence is that the west will no longer have a good reason to convince countries to abandon their nuclear ambitions. That means no credible deal for North Korea, no convincing offer for Iran, and even fewer prospects to end the nuclear programmes of Pakistan, India or Israel^[24].

Looking at the ruins of Mariupol or Gaza City, and comparing them to Pyongyang, Tel Aviv or Tehran, many countries will conclude that a nuclear weapon is a better way to ensure security than any piece of paper.

So if the west does abandon Ukraine, game theory suggests that the world should expect a proliferation of nuclear powers. Each will need to learn, as Russia and the US have, to live on the threshold of diastrous confrontation. But research shows^[25] that establishing a situation of reduced risk takes time.

And that could be a time filled with increased potential for events reminiscent of the Cuban missile crisis^[26] – and a growing belief that nuclear war is inevitable^[27].

References

1. ^{^} Budapest memorandum (treaties.un.org)
2. ^{^} a promise to (it.usembassy.gov)
3. ^{^} widely seen as a good idea (www.latimes.com)
4. ^{^} “credible commitment” (www.hup.harvard.edu)
5. ^{^} a matter of international reputation (www.sciencedirect.com)
6. ^{^} Ukraine war: what is the Budapest Memorandum and why has Russia's invasion torn it up? (theconversation.com)
7. ^{^} internationally accepted nuclear arsenals (www.sipri.org)
8. ^{^} often deliberately opaque (www.gov.uk)
9. ^{^} so effective (www.hup.harvard.edu)
10. ^{^} complexity of these rules (www.pnas.org)
11. ^{^} found guilty (www.prosecutionservice.nl)
12. ^{^} including 196 Dutch nationals, (www.government.nl)
13. ^{^} Russian interventions in European elections (www.politico.eu)
14. ^{^} infrastructure in Baltic states, (www.bbc.co.uk)
15. ^{^} murders (www.politico.eu)
16. ^{^} attempted murders (www.bbc.co.uk)
17. ^{^} full-scale invasion of Ukraine (commonslibrary.parliament.uk)
18. ^{^} abandon Ukraine (theconversation.com)
19. ^{^} also suggests (www.sciencedirect.com)
20. ^{^} potentially unreliable (edition.cnn.com)
21. ^{^} aim to develop (www.bbc.co.uk)
22. ^{^} already invaded by Russia in 2008 (www.csis.org)
23. ^{^} partly occupied by Russia (www.bbc.co.uk)
24. ^{^} Pakistan, India or Israel (ourworldindata.org)
25. ^{^} research shows (academic.oup.com)
26. ^{^} Cuban missile crisis (www.bbc.co.uk)
27. ^{^} nuclear war is inevitable (www.bbc.co.uk)