Would mutually assured destruction help or hinder occupation of minor, non-nuclear countries?

Question

Assume the following hypothetical scenario:

There are only three relevant nations, two large ones (A, B) both with nuclear weapons sufficient to destroy everyone (MAD) and a smaller one without nuclear weapons (C).

Further suppose that one of the large nations (A) is determined to conquer C (for whatever reason, but it's a strong one). A may or may not be a democracy but in any case there is a very strong will to invade and capture all of C. The army of A shall further be capable of doing that against the will of C.

B is actually on very friendly terms with C and would like for C to remain as it is. B is on much less friendly terms with A, surely less so than with C. People living in B will probably strongly feel for people in C and therefore B would likely try to defend C. Let's further assume that B and C together are more capable in a military sense than A.

Now I wonder if the mutually assured destruction of A and B actually helps A in conquering C or rather hinders A in doing that or is largely neutral in that regard?

Mutually assured destruction means that A and B should hardly go to full scale war with each other, because that would mean the end of the world. In game theory that is described as a Nash equilibrium.

But what does it mean in this scenario here and how does mutually assured destruction change the equation?

Without nuclear weapons: B would defend C, they would be stronger than A, so A would likely be defeated or decide not to attack in the first place.

With nuclear weapons, there are more (contradicting) possibilities:

• A can tell B to not interfere in its conquest of C or else A would consider that an attack on itself and retaliate. A would basically virtually extend its borders to include C. MAD would mean that B could not attack A, A could successfully conquer C.
• Or B could tell A that it considers an attack on C an attack on itself and is ready to retaliate. B would basically virtually extends its "protection zone" to include C. MAD would mean that A would not attack C in order to avoid total destruction.
• Or both A and B both include C in their MAD and nobody knows what happens.

I'm totally confused by all that game theory and that is where I cannot get to any further. I just want to know if MAD means that small, third, non-nuclear weaponized countries are easy prey, even if (bonus question) in principle they could be part of a defense alliance? Would the situation change if B and C would be in a defensive alliance?

My guess is that it's still like a game of chicken in the end, and whoever hangs on to his life less wins. But what confuses me is that basically anything can happen with some reasoning (see above).

This question is very similar to Does a policy of mutually assured destruction favor rogue states? but in this case here I do not assume that A is a rogue state (just somewhat aggressive and wanting to conquer C otherwise equal to B and there are no madmen involved, just rational actors with specific interests) and it's a specific scenario where a third minor nation is to be invaded. So more specific answers might be possible.

I'm not interested in any special cases here, A could be the US, Russia, China (with more nuclear weapons), C could be Ukraine, Poland, Taiwan, Mexico, ...(or any other small country) and B could be the rest of the world combined in each case. If the outcome depends on specific circumstances just explain to me which they are.

Answer 1

(This is assuming effective MAD parity * BTW, not states with minor nuclear assets).

TLDR: All other things being equal, MAD supports aggressive behavior in non-vital areas.

If BigAggressive (A?) wants to attack Small (C) and BigFriendly (B?) wants to help, it can, should it see it in its best interest, in the absence of nukes.

With nukes you have 2 phenomenon:

• red lines around Bigs attacking each other's territories (to that I will extend umbrella ** zones such as NATO, Warsaw Pact)

• strong taboos/disincentives towards direct Big-on-Big combat or even the possibility of combat. Solely because of MAD by this point, as, per your question, BigFriendly can otherwise beat BigAggressive.

So, anything that is not explicitly under umbrella is fair game to either Big, should they really, really, see an interest in doing so. You may see proxy wars in non-umbrella areas but otherwise no Big-on-Big will happen. That's not to say other things can't be used to put pressure, such as sanctions, but you won't see Big-on-Big.

Now, you might also see some implicit umbrella areas such as say petroleum-producing areas vital to either side. But the rest can be pushed against by a sufficiently aggressive Big, should it really want to do it.

Taiwan as an example.

The US defense posture assumes Taiwan would be defended. However, if China invaded tomorrow, that support can be assumed to be far from automatic, due to China's 300-odd nukes (vs 5K USA). Yes, it would probably happen, but...

Yet, the US's conventional forces could, at this moment, obliterate China's, especially the forces having to conduct amphibious and naval operations around Taiwan.

And the US has increasing concerns about China (whether or not those concerns are justified has nothing to do with this answer). A casus belli around Taiwan, at this point in time of Chinese-US conventional power ratios would be a rational, if cold-heartedly bloody, calculation by a great power seeing the rise of another.

Absent those nukes, the US would be expected to almost automatically confront China, instead of quite probably, so it seems to me MAD is an enabler for aggressive actions in non-vital areas.

Additionally, there's no further to look than the current motivation for this question, the "special military operation" Russia is carrying out in Ukraine. If NATO wanted to, and they seem to, they could easily boot out Russian troops from Ukraine. Or at least strongly threaten to. They do not, and they've gone on the record saying they would not. Again, MAD in action.

* China has 300 nukes. US has 5K. However, given what nukes can do to large cities and the absence of large scale anti ballistic missile systems, 300 is more than enough to destroy the US, so it is an effective parity.

** umbrella : "anything we consider as a direct attack on our territory or allies". Note that Big country can't just extend "the umbrella" to the whole world, the other Big would flip out or ignore that. I.e. if the US had said we consider a Soviet attack anywhere in the world, on anything, to be a red line then the USSR would have ignored it or instead considered it as a red line of its own ("No, you can't have the entire world"). So those would have been NATO and the Warsaw Pact countries, respectively.

Answer 2

Country C should have a military pact with B and host troops will be stationed there. Knowing this, A will not attack C because it leads to MAD.

However, this means that A will be very reluctant to allow any nearby, previously neutral, countries to have military bases of B. Thus, the stable situation is two spheres of influence and proxy conflicts in third world countries.

Answer 3

There's no apriori answer to this. I depends how much B values C as an ally (or at least as not-occupied-by-A) vs risk of nuclear war. Above a certain threshold of affinity/value for C, B will extended its "nuclear umbrella" over C, either as a mutual-defense treaty or less formally. Below that threshold, B will consider C expendable and won't do it.

Of course, in real life there are more options than those, like support a guerilla war in C etc., which fall somewhere in-between all-or-nothing mutual-defense. Then A has to choose e.g. whether to threaten B with nuclear escalation over their guerilla support etc.