Game Theory, Logic of Deterrence, or a World Without Nuclear Weapons?

Maybe the topic might be considered off-topic by some people when looking at my LinkedIn profile, but as a mathematician and physicist by training, I have a nerdy fascination with seeing mathematical concepts applied to human behavior. Game theory, particularly in the context of deterrence, is a prime example of this intrigue. Additionally, as a physicist, I'm captivated by the dual nature of nuclear power, recognizing both its huge potential for good and its capacity for evil.

The global abolition of nuclear weapons is often called for but seems unrealistic. One could also question whether it is universally desirable.

With the invasion of Russian troops into Ukraine on February 24, 2022 , the threats of using nuclear weapons have brought this class of weapons back into the spotlight.

With nuclear weapons, humanity has learned to harness the most powerful natural forces known to us for destructive (but also good) purposes: temperatures up to 100 million degrees, massive firestorms, supersonic shock waves, and radioactive contamination. By detonating a nuclear bomb, humanity can create miniature, fast "burning" stars. The result of using these weapons over densely populated areas would be, depending on the altitude and yield of the explosion, tens of thousands to millions of deaths, as well as immense numbers of burned, wounded, and contaminated individuals.

Putin’s Nuclear Threats and Their Consequences

Indeed, Putin can conduct his criminal war in Ukraine unhindered because the potential for nuclear escalation deters NATO or the USA from direct military intervention. It is probably the first time in history that an illegal war of aggression has been secured by the explicit threat of nuclear weapons. From the Russian leadership’s perspective, this is a reaction to one of the "main military dangers" that the principle of nuclear deterrence aims to address. Section 12 of a decree signed by Putin on June 6, 2020 , explicitly refers to nuclear deterrence as also applying to the "buildup of conventional armed forces by a potential adversary that possess means for deploying nuclear weapons on the territory of states bordering the Russian Federation and its allies, as well as in adjacent waters." Section 4 of the decree states that Russian nuclear strategy should ensure "the limitation of escalation of military operations and their termination under conditions acceptable to the Russian Federation and/or its allies."

Regarding the war in Ukraine, this means that Russian nuclear threats are justified from Russia's perspective by NATO’s presence or intentions to station forces in neighboring states, aiming to increase the likelihood of winning a war arising from this threat scenario. According to Section 3 of the decree, nuclear deterrence involves not only military, technical, and political measures but also diplomatic, economic, and informational measures—essentially nuclear threats and propaganda, which the Russian leadership has used abundantly. In his speech on the day of the invasion, February 24, 2022, Putin threatened the West with "unprecedented consequences "—an implicit threat of using nuclear weapons.

In response to Western economic sanctions, Putin put his "deterrence forces" on high alert a few days later. Animated nuclear strikes on Berlin or London are routine on Russian television in response to the West's reactions to the "special operation" in Ukraine, later reclassified by the Russian leader as a "real war." "No bluff," Putin stated on September 21, 2022, in his speech on partial mobilization, promising to use "all available means" to defend Russia and its people. Prime Minister Medvedev followed up a few days later, saying Russia could use nuclear weapons "if necessary." In early October last year, Putin's "nuclear train" moved toward Ukraine in a very transparent show. Recently, the Russian chief-of-staff announced plans to station short- and middle-range Russian nuclear capable missiles in Belarus .

While many TV talk show experts on the Ukraine war resolutely advise against being intimidated by such nuclear threats and advocate for continued delivery of heavy weapons to the beleaguered country, it is rarely mentioned that this deterrent effect, due to Russia's nuclear arsenal (nearly 6,000 warheads, including about 2,000 tactical ones ), has already taken effect: namely, in NATO’s and the USA's refusal to send their soldiers into the war zone or establish a no-fly zone over Ukrainian airspace, as Ukraine actually requested in April 2022. Thus, the logic of nuclear deterrence already works so effectively that it barely registers in our consciousness.

While NATO may be deterred from direct intervention, the risk of nuclear escalation due to the supply of increasingly heavy weapons (infantry fighting vehicles, rocket launchers, recently even cluster munitions) should not be discounted. This is not a consistent position. Just because the Russian leadership uses the nuclear threat as a psychological weapon against the West supporting Ukraine does not mean the danger itself does not exist. It seems that, since the Cuban Missile Crisis in 1962, the world has never been as close to the nuclear brink as it is today .

The Logic of Nuclear Deterrence

There is a widespread wish to eliminate this class of weapons from the Earth. Many NGOs vehemently advocate for the abolition of nuclear weapons, and over 90 countries have ratified the Treaty on the Prohibition of Nuclear Weapons , although no NATO state (including Germany) or any other nuclear power has joined. In Germany’s case, the government argued that the treaty was incompatible with obligations arising from NATO membership, specifically the nuclear sharing arrangement involving US nuclear weapons stored at the Büchel military base in Rhineland-Palatinate , which in a serious case would be delivered to their targets by NATO-commanded bombers. Apart from the pragmatic argument that a world where the five permanent members of the UN Security Council voluntarily give up their nuclear weapons is yet to exist—even from an ethical perspective, considering both good intentions and the consequences of actions, it is questionable to advocate for a worldwide ban on nuclear weapons. Why?

Recall the basic model of nuclear deterrence, which uses simple game theory concepts e.g. discussed in books like "The Strategy of Conflict" by Thomas Schelling. Let's play out the scenario that the official nuclear powers (Russia, USA, France, UK, China) and the de-facto nuclear powers (Israel, Pakistan, India, North Korea) consider completely dismantling their nuclear weapons. This could achieve a central collective good, namely the liberation from death and suffering that the use of nuclear weapons could bring to the world. However, from an individual perspective, the familiar dilemma of mutual trust relationships immediately arises. This dilemma arises when the potential for A to harm B is as high as the potential for B to harm A.

Trust means: I assume that you will not harm me, even though you could, and even though I know that you know you could. The higher the price of trust, the lower the probability that it will arise, unless accompanying measures are taken to generate trust. In everyday life, we build trust by "talking to each other" and "getting to know each other" – however, the price of trust that arises on this basis is rarely prohibitive. In the nuclear question, however, the price of trust is simply no longer increasable; the price tag bears the untrustworthy inscription: "Destruction". Consequently, A would only disarm if B also disarms, because A knows that once he fulfills the agreement, he would be immediately powerless against B's potential to harm A if B does not abide by the agreement. In the logic of nuclear deterrence, A's life insurance would only consist of having an equivalent potential to cause significant harm to B as vice versa. In the Cold War, the crucial variable in the nuclear game of the superpowers was second-strike capability: If my opponent knows that I can still destroy him even in the event of a nuclear attack, then he will refrain from the first strike.

From this constellation arose military systems such as heavily protected missile silos or nuclear submarines during the Cold War, which were intended to ensure that even after a nuclear first strike, the capacity for destruction remained unacceptable for the attacker for a second strike. The fact that a few days after Russia's attack on Ukraine, France sent its nuclear submarines to the high seas still follows this logic: the price for a possible nuclear escalation is driven up for the potential attacker by signaling defense readiness and uncertainty about the exact location of the submarines. The Russian side, of course, acts analogously: Putin's statement in 2018 that Russia was ready for a nuclear retaliatory strike, even if it could mean the end of human life, was variously interpreted in German media after the Russian invasion of Ukraine as evidence of his "madness". Literally, Putin said about a retaliatory strike from his country : "Yes, it will be a global catastrophe for humanity. It will be a global catastrophe for the planet. But as a citizen of Russia and as the Russian president, I ask: What do we need a world without Russia for?"

However, we should not simply judge such a statement according to the ingrained moral standards of everyday interaction: "What kind of monster is that, who would destroy his own country and with it all of humanity?" Putin's statement is rather a precise move in the game of nuclear deterrence, which differs considerably from the logic of our familiar interaction processes. People who move in a relatively peaceful environment in everyday life find it natural to subtly signal to others that they will not harm them, for example, through a smile, a handshake, or mutual acknowledgement. In the logic of nuclear deterrence, in which Putin was socialized as a former KGB officer (or more likely as GRU officer), this principle does not apply. If nuclear power A does not want nuclear weapons to actually be used against itself or to be forced to use such a weapon, then this state must first signal a willingness to be prepared to retaliate. Within the rules of the nuclear game, what may seem 'crazy' from an everyday perspective is quite rational. It is the game itself that is sick.

This logic, especially between Russia and NATO or the USA, still dominates today, although nuclear doctrines have changed since the late 1960s and, in the case of NATO, are organized according to the principle of 'Flexible Response,' which also allows for limited nuclear weapon use. While in the early days of the Cold War, deterrence was to be achieved by threatening a massive retaliatory strike, today deterrence is seen in the credible threat of even a limited nuclear strike . Deterrence no longer results from the assured destruction of the opponent but rather from the uncertainty associated with the possible use of nuclear weapons.

The Limits of Deterrence

It sheds some light on the "hypersociality" of our species that under these conditions, any semblance of trust could arise between the superpowers of the Cold War. In disarmament treaties since its late period, attempts have been made to solve the trust dilemma by initiating confidence-building measures, such as mutual control of nuclear arsenals. Over time, an atmosphere of nuclear confidence could emerge, motivating both sides to gradually entrust themselves to each other: 'I refrain from using my potential to destroy you because I have come to the belief that you also refrain from using your potential to destroy me,' is the basic pattern of trust-building between nuclear powers. However, such measures have two decisive limits that seem insurmountable:

Firstly, the logic of nuclear deterrence only works among actors who are symmetrical in their interests. That is: If the government of nuclear power A has an equally strong interest in maintaining its state or sphere of influence as the government of nuclear power B, then an approximate balance of nuclear threat prevents the countries from nuclear attack. However, the logic of nuclear deterrence no longer works when the relationship between the actors is asymmetric, such as when a terrorist group possesses nuclear weapons. Terrorist gangs typically do not have a nation in the background whose interests they need to protect, and therefore, they could simply use nuclear weapons without engaging in the game-theoretical considerations that nuclear powers face. Therefore, confidence-building measures are doomed to fail from the outset with an actor behaving asymmetrically to its own interests.

Hence, it is absolutely essential to prevent such actors from obtaining nuclear weapons. It is known that the terrorist group Al-Qaeda sought nuclear weapons . The purpose of the 2015 nuclear agreement with Iran, which was terminated by US President Donald Trump in 2018, was to prevent the enrichment of weapons-grade uranium necessary for building a nuclear bomb. Finally, Iran has not only threatened Israel with nuclear annihilation, but, from the perspective of the USA, given the dominance of the Islamist regime of the Mullahs, it cannot be ruled out that weapons-grade uranium (or the means to obtain it like e.g. centrifuges) might fall into the hands of Shiite terrorist groups.

The second limit of confidence-building measures comes into play when the major nuclear powers would consider actually relinquishing their remaining nuclear weapons after a significant reduction. Suppose the number of nuclear warheads had been reduced to about a thousand (currently around 12,500, at the height of the Cold War it was around 70,000). These states are now faced with the question: Do I actually risk depriving myself of my second-strike capability and thus making myself vulnerable to a potential opponent, giving them the opportunity to attack me with nuclear weapons without significantly altering their calculus in my favor, by completely giving up my nuclear arsenal? If one thinks this situation through to its logical conclusion, it becomes clear that a ban on nuclear weapons must ultimately fail.

No real Ban in Sight

The Nuclear Non-Proliferation Treaty, which came into force in 1970, obligated the nuclear powers to the ultimate goal of complete nuclear disarmament. In return, non-nuclear-weapon states committed not to pursue nuclear weapons themselves. India, Pakistan, Israel, and (more recently) South Sudan did not join the treaty; North Korea withdrew in 2003. However, today the number of nuclear warheads has only been reduced, while the arsenals are simultaneously being modernized, and not completely abolished, as the treaty envisages. China, up to now the only state that has ruled out a first use of nuclear weapons, is currently even rearming , and Putin recently suspended the New START Treaty on the limitation of strategic nuclear weapons after the USA had already terminated the 30-year-old INF Treaty on the renunciation of land-based intermediate-range nuclear missiles in 2019. The USA justified this by accusing Russia of violating the agreement.

These extremely alarming developments, and in particular the lack of adherence to agreements by official nuclear powers, can be scandalized given the significant importance of the issue for all of humanity. However, they are ultimately rooted in the trust dilemma outlined above. The reduction and non-proliferation of nuclear weapons can, assuming confidence-building measures, be reconciled with the logic of deterrence. However, this is not the case with the abolition of nuclear weapons. Already out of self-interested state raison d'etat, it would be highly unwise to give up one's nuclear arsenal without being completely sure beforehand that a potential nuclear-armed opponent has also completely dismantled its arsenal. But perfect security will never be objectively and, above all, subjectively attainable if the price is that the most monstrous weapon on this planet could hit one's own nation. The trust dilemma thus becomes fully effective once a certain point of nuclear weapons reduction has been reached and undermines the goal of nuclear disarmament.

"The nuclear capacities of the nuclear powers would still be sufficient for multiple overkill (i.e., the multiple destruction of the opponent)."

For the major nuclear powers China, Russia, and the USA, this point will probably be the moment when further reduction of nuclear weapons would prevent effectively retaliating against a nuclear-armed attacking nation—because this is the core basis of the deterrent effect of nuclear weapons. Even the New START Treaty only envisaged a reduction of the strategic arsenal to 1550 nuclear warheads—a significant step for nuclear powers whose nuclear capacities would still be sufficient for multiple overkill (i.e., the multiple destruction of the opponent).

However, overkill capacities are not simply "irrational" or "wasteful" in the logic of nuclear deterrence. Rather, they ensure that all relevant targets in the opponent can still be reliably hit even if there is a significant reduction in second-strike capability due to a first strike or a significant number of nuclear warheads fail to reach their target due to defensive measures. Therefore, there must be enough overkill capacity so that the opponent can still be completely destroyed at least once. The trust dilemma thus makes it highly unlikely that a reduction of the nuclear arsenals of the major nuclear powers Russia and the USA will occur below a multiple overkill capacity, even if, by some miracle, all geopolitical tensions between the USA, Nato and Russia or Israel and Iran were to dissolve into thin air.

On the Ethical Side of Things

It is not only unwise for nuclear powers to relinquish their nuclear arsenals; it is also morally irresponsible with regards to global peacekeeping and the promotion of a more liberal international order. Often, the argument is made that during the Cold War, nuclear weapons ultimately served global peacekeeping because the cost of a nuclear war is prohibitive, and therefore, assuming a balance of terror ("mutual assured destruction"), they acted strongly to dampen conflicts. In this logic, the abandonment of overkill capacities between Russia and the USA would have promoted a nuclear war—or even conventional attacks—because the reduction of second-strike capability would have lowered the thresholds for the use of nuclear weapons. But even in today's times, the possibility of a potentially limited use of nuclear weapons due to the overwhelming destructive power of this weapon type and the unpredictable escalation potential presents an extremely high barrier with potentially pacifying effects. Killing several million people with a single bomb would create such a novel situation in world history that no actor knows how other actors would react to such a situation: with absolute submission? With unprecedented self-destructive revenge desires? The socio-psychological dynamics after a nuclear weapons attack, which far exceeds the explosive power of the bombs in Hiroshima and Nagasaki, are terra incognita—and uncontrollable. This maximum degree of uncertainty significantly raises the threshold for a warlike confrontation between nuclear powers.

However, on the path to a possible abolition of nuclear weapons, another issue arises. If one consistently follows through with the demand for a global ban on nuclear weapons, this could lead to a world dominated by only one state, namely the one that most ruthlessly abuses the trust of all others and, despite the assurance to abolish its nuclear weapons, does not keep its promise or secretly retains stocks. The abolition of nuclear weapons may be right in an ideal world—but in the real world of geopolitical calculations, it would be just as undesirable for increasingly manifesting into a dictatorship Russia to be the only nuclear power, as it would be for the imperial USA with its around 750 military bases scattered around the globe or the completely anachronistic, still infected by communist personality cult, militaristic North Korea.

If power corrupts and absolute power corrupts absolutely, as Lord Acton said, then it is imperative to prevent there being only one nuclear power. Twenty large nuclear warheads in the hands of a single nation would be enough to keep the rest of the states on this planet under the yoke of the threat of such sensitive nuclear strikes that this nation could seize uncontested global domination. Thus, the question of the abolition of nuclear weapons not only acquires a purely instrumental-strategic significance but also contains an ethical component. If we do not want to live under the unbroken influence of a single geopolitical actor, then the nuclear weapons ban treaty or the vision of "Global Zero" already introduced by Barack Obama should not be pursued further. It is hard to imagine that the abolition of all nuclear weapons is something we can still collectively desire, even when considering the generalizable consequences of this desire.

As perverse as it may sound at first glance, the conclusion suggests itself: To avoid the abolition of all nuclear weapons is—not only a matter of national egoism of nuclear powers in the "real" world characterized by interests and uncertainty, but it is also in the collective interest, even of states that currently do not possess nuclear weapons and do not aspire to do so. At the same time, it is in everyone's interest that the barriers to the use of nuclear weapons are by no means lowered, as the USA has been aiming for since 2016 with the renewed development of "mini nukes " that are significantly below the destructive potential of the Hiroshima bomb.

Is all of this an intolerable burden that cannot be increased? Yes, it undoubtedly is. Preventing further proliferation of such weapons is as much a dictate of reason as it is right to work towards reducing these weapons in individual nuclear powers, which in turn serves the goal of non-proliferation. The demand for a total ban on nuclear weapons is often raised in the face of grotesque near-catastrophes and is readily underpinned with the corresponding moral fervor. However, upon closer examination, it seems more like a "brilliantly organized advertising campaign that, defiantly and without regard for adverse realities, engages in security policy storming with a sense of moral superiority." The tension between the desirable good and the bitter reality of the bearable, measured against this good, is nowhere as pronounced as in the question of how humanity deals with its potential for self-destruction. Advocating for the complete abolition of nuclear weapons may seem good at first glance—but ultimately, it cannot be justified.