1. Introduction

We live in a time when Russia has started an unjust war against Ukraine. Russia is capturing and destroying Ukrainian cities, killing and torturing its citizens. They want to break the entire nation, repress its culture, and put Russians in the place of Ukrainians. To achieve this they use all kinds of terror, they ignore any rules of war.

One of the reasons Russia is able to do so is the possession of an arsenal of nuclear warheads, the largest in the world. They have enough to destroy the entire civilized world, to make it uninhabited land. This ability became their national pride, their glory, their pretext to claim dominance in the world. And they keep reminding it directly or indirectly over and over again.

Every man understands — it is a threat. And it does affect the decisions people make. But a nuclear strike can cause retaliation from the democratic world, so that Russia won’t exist either. So how do we value this threat? Let’s put aside questions about moral grounds and consult the game theory.

2. Game theory

For simplicity, assume we have three players:
Player A - the democratic world (USA, EU, their allies)
Player B - Russia
Player C - Ukraine

There is also China, but it’s not an active player here, since it avoids nuclear rhetoric and it’s not a public ally to Russia.

Note that Russia denies any sovereignty of Ukraine. It treats it as a resource, which can be controlled either by player A or player B. From Ukraine’s perspective, it decided to ally with the democratic world.

In our simplistic model, we can accept the Russian attitude and treat C as a neutral resource, the battle for which is ongoing. As a Ukrainian, I know how far this is from the truth, but it’s reasonable to accept Russia’s view because we’re gonna analyze their strategy here.

It’s absolutely clear that player A has much more resources under its control than player B. This also means that it has much more to lose than player B.

Note that in this game players don’t want to maximize just the value of resources under their control. They also want to maximize the relative value, the percentage of control. Because, clearly, any war causes an immediate loss of value for all players. But rational players want to raise their value in the future. And dominant players want more percentage. No doubt, Russia is seeking dominance, not just prosperity (there were many Russian billionaires in the world before this war, and Russia still has a huge amount of natural resources).

Without additional assumptions, the nuclear annihilation is a reasonable option for an underdog player who seeks dominance, but can’t see any other way to gain more of it. Simply because it equalizes everything. And humans are capable of such actions. For example, an abusive male can kill a disobedient female — and ruin his own life because of that. Recall that Russia’s ruler has already compared Ukraine with a disobedient woman (and himself with a rapist).

The question then becomes the following:

What losses an underdog, seeking dominance, can accept before choosing suicide?

Unfortunately, game theory ends here. To answer this question we need to know psychology, history, culture, and many many other facts relevant to this war.

3. The prognosis

Rapists can kill, but they don’t do suicides. They want to live. They can choose wrong actions, but not because they’re irrational. It’s because they are not smart enough. Russia was not smart enough to start this war. But I’m sure it is not that stupid to go suicide because of the loss.

Russia attacked not because of desperation, not because of its humiliated position in the world after the USSR collapse (ignore Putin’s whine about humiliation, it’s a trick called “I’m a bully that plays victim”). Russia attacked because it thought it could win. They have many victories before this war. The biggest one is Trump as a US president (but it turns out Ukraine has a Joker).

You don’t go suicide just after you thought you can conquer the world and indeed had your chances (Hitler doesn’t count, he’d be executed anyway). Thus, the world should not fear Russia’s nuclear terror. Isolation by North Korea example is the equilibrium in this game, in my opinion.

There is one question left — about the nuclear attack on Ukraine. In essence, Ukraine is a hostage under the gun of a terrorist, wearing a bomb vest.

Will the democratic world cause a nuclear exchange if Russia uses a nuclear strike on Ukraine? If we accept that Russia is not suicidal, then the answer must be affirmative (though I’m not unbiased here). Otherwise, the terrorist can use the same tactics to conquer any other land, including NATO countries. Why start the nuclear annihilation of the entire world over Estonia, for example, after Ukraine is nuked without retaliation?

Despite my confidence that there won’t be nuclear strikes, I think that Russia will provoke direct NATO involvement one way or another — to avoid humiliation by the Ukrainian army. It seems that an accident at Zaporizhzhia nuclear power plant, the biggest in Europe, is the cause they are seeking. But let’s hope it won’t happen as in Chornobyl. Ukraine doesn’t deserve the second one.