Putin’s nuclear threat according to game theory

We have the Doomsday Clock. In 1945, the scientists who, directly or indirectly, like Albert Einstein, helped develop the first nuclear weapon, founded the Bulletin of the Atomic Scientists, and two years later created the Doomsday Clock. It’s not a physical clock, it’s an idea that collects in minutes and seconds the time left until midnight, the end of the world. These dark hours are a metaphor for the risk of a nuclear conflict that ended civilization as we know it. At the beginning of each year, an official statement is issued indicating whether we are ahead of the seconds or behind them.

Mikhail Gorbachev’s perestroika bought us time, and the collapse of the Soviet Union became the farthest point of judgment. Since then, every year it has been approaching 0:00, also due to the inclusion of new risks such as global warming, more countries joining the nuclear club and the development of new weapons.

At the beginning of 2022, the clock showed only 100 seconds to midnight, but few media picked up on this, the feeling of the risk of nuclear war seemed to have disappeared.

Mutual Assured Destruction Doctrine and Mathematics

A chance meeting at Princeton University between two refugees from Nazism led to a collaboration that ended with the publication in 1944 of an amazing book: Game theory and economic behavior. The authors were the Hungarian mathematician John von Neumann and the Austrian economist Oskar Morgenstern. Game theory opened up a field of mathematics that was supposed to serve to evaluate human actions in various situations. The main area of ​​application was the economy. However, the method has spread to other areas, and one of them is war.

After World War II, the same game theory led John von Neumann to propose the Mutual Assured Destruction Doctrine (MAD, an English acronym that also means “crazy”). According to MAD, if the US (and NATO) and the USSR (and the Warsaw Pact) had enough nuclear weapons to kill the other, they wouldn’t use them because it would be self-destructive. Despite the fact that the world was on the edge of a knife, then the world experienced an unusually long period.

Since 1986, the number of nuclear warheads has been declining, although there are enough of them left to bring the entire planet to catastrophe.

But the balance postulated by MAD is shaky. The situation changed on February 24, 2022 with the start of the Russian invasion of Ukraine, and Putin took it upon himself to remind us that the risk of using nuclear weapons still exists.

Scenarios according to game theory

The invasion of Ukraine, which seemed to be a military parade, turned out to be a fiasco for Putin. The weaknesses of her army and her inferiority in front of Western weapons are revealed. Even taking into account that propaganda in wars makes it difficult to know the truth, it is clear that Ukraine, at the cost of great lives, is reclaiming part of the occupied territories with some undeniably successful operations, such as the partial destruction of the bridge of Kerch, which unites Crimea and Russia, what will happen if Ukraine attacks these direction will continue?

Game theory can give us some clarity. Consider three scenarios:

1. The war has taken root and continues indefinitely.

2. Russia launches a major offensive and forces Ukraine to accept Putin’s terms.

3. Ukraine, with the help of the West, manages to expel the Russians from the occupied territories.

The third option is ideal for many. Perhaps Russia will come to terms with the situation, but defeat is more important for Putin here. When leaving the occupied territories, the reactors of Zaporozhye could be destroyed. It would be a desperate move that would not give him any advantage and would not prevent his fall, and, moreover, the infection would touch Russia. We could suggest to Putin in this situation to resort to the use of nuclear weapons. Russia has a gigantic nuclear arsenal that it can use against a NATO country, but in this case, mutual destruction is guaranteed. For this reason, this route seems to be excluded.

Most Likely Scenario: Tactical bombing

But what happens if a tactical weapon (a small nuclear bomb) is used in the territories reclaimed by Ukraine, which Russia considers its sovereignty?

Formally, although illegally, Russia included them in its territory. According to its doctrine, one of the cases when it provides for the use of nuclear weapons is aggression against the Russian Federation, even with the use of conventional weapons, if the existence of the state is threatened. restoration by Ukraine of these territories in Russian legality can be seen as a threat to the Russian Federation.

A thermonuclear bomb uses deuterium and tritium, which are activated by less than 10 kg of U-235 or Pu-239. These isotopes must be in very high concentrations, several times higher than those found in nuclear reactors, and, fortunately, extremely difficult to obtain. In fact, Russia and the United States have not been producing them for decades, enough with what is available.

Fission of U-235 or Pu-239 produces mainly short-lived isotopes that decay in a few minutes. The same happens with the released neutrons, which activate some materials that become radioactive within a few hours. Destruction is caused primarily by the release of energy. Smaller ones (1 kt or less) are similar to conventional bombs, but with much more destructive power. The consequence of this is that the country that launches them is not afraid of infecting their own territory, so it is not a problem to use them within their borders or nearby. It is estimated that there are about 2,000 weapons of this type in Russia, but one is enough to change the rules of the game.

Russia could use these bombs in areas with low population density and, even if it did not result in thousands of deaths, the propaganda effect would be uncontrollable. We would enter a realm of uncertainty, and at best, perhaps the cataclysm would be purely economic.

The European Union must prepare joint action in this case. In essence, an agreement including as many countries as possible is necessary to isolate any state using this type of weapon. In a post-nuclear world, we would all be losers.

Best in Game Theory

One version of game theory is the cooperative games popularized by the movie amazing mind tells about the life of its main creator John Nash.

Applying co-op games to the current situation would probably lead us to the least bad option, which is negotiating with Russia to avoid the nuclear option, rather than expel Russia from all the territories it occupies, which have also been at war since 2014. .

Putin, before he was expelled and resorted to nuclear weapons, would have agreed to negotiations. Ultimately, ending the war, even if it means some unfair concessions for Ukraine, will ultimately backfire on Putin.

In risk-benefit analysis, game theory tells us that negotiating with Putin is the least bad option, but it is a tightrope game.

In any case, we must return to the path of reducing nuclear weapons: those who have them can use them to blackmail those who do not. Otherwise, we will witness a new nuclear race, to which new states will try to join. The doomsday clock will tick faster than ever before midnight.

J. Guillermo Sanchez Leon, Mathematical Modeling. IUFFyM, University of Salamanca

This article was originally published on The Conversation. Read the original.

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