Arms races are often decried as expensive, counterproductive (the more you arm up, the more your opponent arms up) and so forth. However - what is the alternative?
I am not referring to situations in which an arms race is merely frivolous - say, two nations just wanting to have a dick-waving contest - but rather, that suppose you have an aggressive, perhaps even genocidal, adversary that is full bent on conquering you in the immediate near future whether you like it or not. (Suppose, for instance, you are Poland in 1938, but with the benefit of hindsight - although going with a pure hypothetical might be better, so as to not turn this into a WWII thread.) What alternative do you have other than an arms race?
Let’s suppose, also, that you have no allies you can count on, either, so you can’t call any other nations for help if attacked. Under such circumstances, what could you do other than arm up? If you say, “I refuse to play this arms race game which is expensive, I would rather spend this money on other governmental-budget priorities”, then you’re going to get blitzkrieged.
So the only way to save yourself is to arm yourself? Addressing the reasons for your neighbors’ genocidal tendencies is out of the question? These people are so Romulan in their desire for war that there is no hope of a negotiated peace?
Bullshit!
There are always other options than war. You might not like it. It might be messy. It might take sacrifice and humility and even, god forbid, deference. But there are ways other than war.
Could you give some examples of countries with “aggressive, perhaps even genocidal, adversar[ies]” where people are arguing to abandon an arms race?
The alternative in most situations is arms deals, diplomatic pressure, and, baring those extremely rare genocidal neighbours, setting the limit you are willing to spend somewhat lower, and hope that, should your opponent keep growing their arsenal despite yours plateauing, your economic advantage will allow you to quickly increase your forces should your cold war turn hot.
Of course, if the hypothetical you wish to go with is “What’s the alternative to an arms race if not playing the arms race is being attacked and defeated” there’s not really much to discuss.
The usual use of the term “arms race” is precisely about the futile zero-sum kind where both parties would, viewed in isolation, prefer to not be in the race. The situation the OP posits may be arming in response to a threat, but it isn’t a rhetorical “arms race.”
If what you OP really mean is “What’s the alternative when living next to an avowedly imperialist power that wants your land?” here are some ideas:
A high quality secret service and selective assassinations of the most bellicose politicians on the other side might be a way to do that on the cheap. See Mossad, especially in their early days.
Obtain nuclear weapons. See North Korea, Pakistan, Iran, South Africa at one time, and presumably / possibly Israel. Nukes aren’t cheap, but they buy a lot of deterrence for relatively little treasure.
As others have said, the usual way to win an asymmetric game is not to play the one the opponent wants you to. See asymmetric warfare, but the idea is not limited to the strictly martial realm.