Nuclear War and other Bad Things. Probabilities and a Bit of Game Theory.

Tom Kando

I continue to fret about the war in Ukraine. I worry about Putin's nuclear saber rattling.

All the pundits keep reassuring us that this is mere bluff and  that there is very little chance of this war escalating into nuclear Armageddon. Most of us don't have sleepless nights worrying about the possibility of nuclear war. Many of us did, during the Cuban missile crisis, but not now.

 Let me try to approach this topic with a statistical or a game-theoretical mind. Here are a couple of thoughts:

1. The probability of a  bad event  happening should be inverse to how terrible the event is likely to be.  Put differently, the greater a  risk is,  the smaller the probability of failure, when taking that risk, should be.

For example, it is possible that I will catch a cold this winter. If a doctor  told me  that there is a probability of .33 (one out of three) of this happening, I will not worry very much. On the other hand, if someone told me that there is a .003 probability of nuclear war  in the coming six months (one out of 300), I would worry quite a bit.

In other words, the greater a possible upcoming catastrophe is, the closer to zero its probable occurrence should be.

I have no idea whether there exists a   negative correlation between how terrible  an event is and how likely it is to happen.

One important aspect is  the time frame: Is the bad thing likely to happen  soon or in the distant future?  The catastrophes which Hollywood likes so much - giant earthbound  asteroids, devastating earthquakes, etc. - have the advantage of following geological and astronomical timetables. We don't worry about them, in the belief that they only occur once in a million years. What about global warming - the destruction of the planet? This may be the worst thing that can happen to  us, and its likelihood  is quite high. But it is happening gradually. We are the slowly boiling frog.

2. Getting back to the topic of nuclear war, a simple game-theoretical approach occurs to me. Consider the two-by-two table below: 

		Country A
		Has nukes	No nukes
Country B	Has nukes	1. Nuclear Peace?	2. B attacks A
	No nukes	3. A attacks B	4. Only conventional war

Analysis:

Cell 1: This is the current situation  in the world: The two opposing enemies - NATO and its opponents (including Russia and North Korea) - both have nuclear weapons. Neither uses them, so far. They both  abide by MAD - Mutually Assured Destruction. This is the Nash Equilibrium, which is a stalemate whereby Ano participant can gain by a unilateral change of strategy if the strategies of the other(s) remain unchanged.  For example, Putin must assume  that if he were to use nukes, the West would react in kind.

Cell 2: This is what happened briefly at the end of World War Two: One side (the US)  had a monopoly on nuclear weapons. It used them to defeat its enemy, which did not have nuclear weapons. Had Japan possessed nuclear weapons at the time, President Truman would probably not have used them.

Some argue   that if A has a monopoly on nuclear weapons and knows that B cannot retaliate, then  it may not need to use nukes in order to win. The threat alone may be enough.

Cell 3: This might have happened at the end of World War Two: If Germany had succeeded  in  developing nuclear weapons before the allies did, Hitler would have used them. He used his V1 and V2 rockets, and he  searched desperately  for his  >Secret super weapon." 

Cell 4: This was the world before the genie was out of the bottle: No nuclear weapons, no nuclear war, only conventional war.

Conclusion:

Experience shows  that when only one side  possesses nuclear weapons, it is likely to use them.

When both sides possess nuclear weapons, the prediction is more difficult. So far, both sides have used restraint. It is sometimes said that the existence of nuclear weapons  has saved the world from a third global war...

So far, the world has enjoyed  the Nash Equilibrium. However, the situation could turn into a   prisoner=s dilemma: This occurs when each individual side acts  in what it believes to be its own rational self-interest, but ends  up harming everyone=s collective interests . This is most likely to happen when neither side knows what the other side=s move will be.  The example often given is that of a couple of criminal partners who separately snitch on each other. In this example, neither convict knows what the other one will do.

In the confrontation between Russia and the West, both sides know at least what the other side=s nuclear capacity is, even though neither side knows with  certainty  what the other side=s move will be.

It isn't  clear that all the political and military leaders who have access to nuclear weapons will always use restraint. Had Hitler possessed nuclear weapons,  he would probably  have used them, even knowing that the allies also had them.

Putin may not be another Hitler, but are we sure that he is just bluffing?  Then, too,  there may be  other men in the Kremlin who are even more bellicose than Putin, and even more eager to press the button, come what may.

Finally, there is a  proliferation of nuclear weapons to additional  countries. So far,  nine   states have nuclear weapons: the US, Russia, the UK, France, China, India, Pakistan, North Korea and Israel. Iran may soon join the list and others may follow. There is no guarantee that there will never be a nuclear attack emanating from one country or another, launched by some leader(s) with a deranged mind(s), or even accidentally. leave comment here