Rye: interesting post.
I may not have fully understood you though.
If the perception of A by B as a mortal enemy exists, then I don't think B really has the choice 1.b2 (accept that A's edge exists, when A has only hinted and not demonstrated it). What is the real difference between 1.b2 and Case 2 in your model? Is it the political pressure that the citizens of B will mount on their government if A openly demonstrates its edge as in Case 2?
Anyway, here's my take on your model as I understand it... please correct me if I'm wrong anywhere.
Following your premise, A and B are nuclear armed "mortal enemies". B's nuclear arsenal poses an existential threat to A if used, much more so than A's nuclear arsenal poses to B. Therefore A has to come up with SOMETHING (technology, stated policy, actual policy, or whatever) which neutralizes the advantage B has over A.
An obvious real-world application of this model is: India= B, Pakistan=A. Imaginary applications include nuke-armed Iran=B, Israel=A. Also nuke-armed Japan/ROK/US= B, DPRK=A. (Am I being true to your model by casting these nations as "A" and "B" here?)
Maybe it could even be extended to PRC=B, India=A... and USA=B, PRC=A.
Anyway...
In Case 1, A hints to B that it has such an advantage. In Case 2, A actually demonstrates it to B.
Case 1 (A hinting at an edge over

, I think, would leave B with three choices...
1.a: Calling the bluff. This is where B says "b@lls, A doesn't have any kind of edge over us", and then *B continues to formulate and act on policy as if A didn't have any kind of edge*. This is a risky path, and I don't think even the most crazy Mullah government would take it without a backup plan.
Rhetoric is another matter... B might SAY they disbelieve A for purposes of public consumption... but it shouldn't be confused with ACTUALLY calling A's bluff.
1.b: B can *formulate and act on policy, henceforward, assuming that A does in fact have an edge*. In three broad ways:
1.b1: as in your model, B acquires the technology to "counter" the greater threat from A that has been hinted at. Example... if a nuclear-armed Iran could buy or build foolproof cross-theatre defence to protect itself from Israel's far larger and more powerful arsenal.
1.b2: B could push A to test and show their hand, thereby gaining diplomatic leverage and decreasing international opprobrium as they pursue either a defensive or offensive counter to A's edge.
This *may* have been what Iran was trying to provoke Israel into with the Hezbollah high-jinks earlier this year.
It is also what was successfully achieved by India w.r.t. Pakistan in 1998 (Pokhran 2 followed by Chagai Hills in Pavlovian fashion). In the Pakistan-India example, Pakistan is "A" because between its use of terrorist proxy war, and its combination of basketcase economy plus jihadi tendencies (what Johann describes as "suicide bomber on hospital bed"), it had cultivated an *image* of being the mad-nuke-bomber-with-nothing-to-lose. From '87 to '98 it was able to blackmail India thus by using hints, i.e. ambiguity.
The 1998 tests by India set in motion a process to end that ambiguity. This had mixed results. It caused sanctions to be clamped which hurt the Pakis much more than they hurt us. It also justified our own tests in retrospect very quickly, once the Pakis had tested.
However, it also engendered an international media and diplomatic whinefest about the "South Asian Nuclear Flashpoint", reinforcing equal-equal. Pakistan sought to take advantage of this by initiating Kargil in the hope of "internationalizing Kashmir". (It didn't work out that way for Pakistan, but that's a different story).
Also on the negative side for India, it made common knowledge of the fact that Pakistan was a nuclear suicide bomber on a hospital bed with real nukes... a critical fact in determining US policy towards them following 9/11.
All told, it failed to end Pakistan's combination of nuclear and subconventional (terrorist) blackmail against India. However, it has ended up making it less easy for TSPA to support terrorism against India as openly as pre-1998.
In the most general terms, 1.b2 is designed to either show that A does not have the edge or to demonstrate conclusively that it does, thereby depriving A of any advantage that ambiguity might bring.
1.b3: B could go ahead and nuke A with everything it has, and let Ram sort them out

After all, A has only hinted, not shown what it has. B is not sure that A would have an advantage, but fears that A might. What B IS sure of, is that with its own arsenal it could finish A existentially.
If it struck first, struck hard and without warning. So why not go ahead and use it?
There will be major repercussions for B probably... on the economic, diplomatic, technological, political fronts for sure. Maybe even on the military front, with retaliatory strikes from hyperpowers C and D. So this is also a risky path... but NOT so risky as 1.a which is pure bluff calling.
This is an option B will explore only when other factors regarding its interaction with A cross a tolerance threshold. That is, when the pain of possible repercussions would be less than the pain of dealing with A in its present and capable form.
All told, the Case 1 scenario where A maintains ambiguity doesn't totally secure A. It makes B more insecure, certainly. But unless A can feel absolutely sure that B could (1.b1) never acquire a technological capability that neutralized their edge, or (1.b3) feel tempted to use what it had in order to end the game once and for all, A really hasn't become more secure as a result of its own ambiguity. Has it?
Case 2: A actually demonstrates its capabilities to B.
The outcome of this is of course subjective. In the case of Israel, if they could demonstrate the sub-based 2nd strike capacity that Sadler talks about, that would probably shut Iran and Syria up for good. Which is why I am puzzled that they don't do it.
On the other hand. If Pakistan demonstrated possession of thermonukes, or signed an open agreement with KSA to host their second-strike capability (instead of merely hinting at the existence of such an agreement)... it would certainly push India in one of two directions.
2.a First- B responds to A with capitulation (In India's case, acceptance that Pakistan is untouchable, and has an advantage forever as you said). I don't think this would ever fly in a democracy like India, given what is at stake, but I could be wrong.
2.b Second- this is identical to the 1.b3 scenario. B hits A with everything it has and damn the consequences, because they couldn't be worse than capitulation.
Pakistan is not likely to ever have a true second-strike capability from submarines or any such thing, but if the GOI has reason to believe completely that a second-strike-arsenal-hosting agreement with KSA in the works, we might decide to go ahead and finish Pakistan before it can come to fruition with a massive first strike. Given India's soft-state tendency to comply with international opinion, though... there is no guarantee that the GOI won't choose capitulation over this option. Especially as long as we have an NFU doctrine.
Pakistan is aware of this, and doesn't want to push India to the point where it has to make that choice (perhaps some in the ISI do, but not the TSPA in general as of now).
Instead, even though we pulled a 1.b2 on Pakistan and made them demonstrate nuclear capacity... they continue with "hinting" at more and more "edges"... such as seeding rumours of deal with KSA to host their second-strike arsenal, and suggesting the possibility of a JDAM. They also continue with "demonstrating" more "edges"...whether real or imaginary... such as by firing off "Baburs", Dingdongs, and assorted Gleen-Paintee-Chinee-Delivelee.
Given the behaviour of the MMS government, it is certainly looking as if India is leaning more towards 2.a than 2.b. But of course, there is a wide space in between those extremes, and we haven't capitulated yet.
2.c Third- B can in turn, "demonstrate" its ability to counter whatever advantage "A" has demonstrated that is possesses. I have put this option in for the sake of completeness, because even the US has not been able to carry out an NMD test with sufficient success to demonstrate any such ability.
Have I missed anything? Or have I mauled your original model beyond recognition?
Sadler, thanks for your responses... they are a lot to think about. Given Rye's model, do you still think it would be in Israel's interest to test even if Iran tests? Would you want to be provoked into showing your hand, if ambiguity is working well for you? I ask because Israel is a nation of sensible people, unlike Porki-land which couldn't help testing in response to India's 1998 tests.