If there is a war between two countries with time travel capabilities, during both the lead up (cold war style) and during the fighting would either side be prevented from using time travel to achieve a quick victory? What would be the necessary laws of time travel to prevent this from happening? Possibly by ensuring mutual ensured destruction.
MAD happened with nukes because both sides could see a first strike coming with enough time to launch a second strike before the first strike hits.
For time travel to have any MAD restrictions, you need a similar ability. So the rules of time travel would have to allow:
Detection of temporal incursions. You don't need to necessarily know when and where they went to, but you have to know in the present when such an act was launched.
It could be a particular energy signature or tachyons or whatever technobabble you feel like using. So long as neither side can prevent the detection of their breaching of the fabric of time, it will work.
The "time" to launch your own temporal incursions before changes caused by the enemy's team would overwrite you.
There are several ways to achieve this one. You could have it that changes in the timeline do not propagate instantly; it takes some "time" for time changes to reach the present. Or you could say that the temporal war departments have the ability to shield particular areas from changes in the timeline, thus preserving their ability to respond and retaliate. Or something of the sort.
The thing about time travel is that generally, the first side who invents it (and is willing to brave the repercussions of making major changes in history) effectively wins. With nukes, both sides had the ability to create them years before either side had the ability to assure the destruction of the other.
So if you want a MAD-style stalemate with time travel, you somehow need both sides to invent it simultaneously. Alternatively, one side (or both) could lack the willingness to use it militarily unless they had no other choice, which would allow the other side to develop the tech, leading to a stalemate.
I'm inclined to think that, much like other innovations, in developing time travel technology and weaponizing it nations would develop means more sophisticated and predictable than just going back in time and attempting to change things in their favor.
For example instead of going back from the present to the past, how about taking moments from the past and bringing them to the present day? This can be in the form of detonating a bomb in a city or somesuch and copy-pasting prehistory over the top of it, to see what this would look like search for the "Call to Power 2 Eden Project" on youtube. Or if you want to be really naughty, you can pinpoint the time and location of a severe natural disaster in 'enemy territory' and bring that over to the present day in order to cause all sorts of difficulties not immediately identifiable as the results of time travel. Volcanic eruption? Tsunami? Asteroid impact?
It would be a "safe" weapon in that the user wouldn't have to be concerned about altering the timeline in unpredictable ways, but at the same time it has the potential to cause significant damage and loss of life, so in this case MAD would absolutely apply.
MAD would not apply
The many-world interpretation of quantum physics could (in some interpretations) prevent things like the grandfather paradox from happening by dictating that if one were to go back in time, the timeline would diverge, making an alternate universe of sorts that would be affected by the time traveler , but the original timeline would remain .
Given an the infinite nature of a universe with time travel, we must assume that an infinite number of time travel events have occurred, attempting to change the past. We must also assume that an infinite number of time travel events have occurred, attempting to overturn or circumvent these previous incursions.
So, our current timeline is the result of an 'infinity war' which is still being fought. Any attempt to time travel will dump the traveler into a high-tech military situation filled with bloody conflict, bubble-world isolations and inception-like realities, which underpins everything that we know and also supports the timeline of a elite, society in the future which has destroy all other time-traveling societies, past and future.
So in the context of MAD, as soon as time travel becomes an inevitability for your race, your race is immediately destroyed, mind controlled, incepted, isolated, or given cheap HBO and MTV. This would leave your technologically advanced overlords untouched (as well as unnoticed) and not mutually destroyed.
You may also find that reality was actually a carefully constructed and maintained environment, dutifully looked after by an extremely advanced race who are totally dedicated to protecting it from you, your intentions, and the possibility that any of this would ever be revealed to the poor unknowing captives in the "real world".
Interesting questions you have there cadet, here at SpaceCore™ we pride ourselves in our understanding of how our temporal physics work, so lets see if we can answer your questions in turn.
Now, you may be wondering why our enemy, the Hyluians, don't simply travel back in time with their time-space gun and simply kill off the first human, or maybe steal their rattle. You see, both we and the Hyluians developed our temporal tech at roughly the same time, mostly because we stole ideas from each other, but as you already should know, under Page 22 of temporal mechanics, we cannot travel back to earlier than when we first setup the very first temporal device.
Now, there have been rumours going around that Hyluians have found some way to bypass this, however, our crazy boffins down at the SpaceCore™ Temporal Physics Institute have developed what is known as 'temporal shielding'. You may have heard the term thrown around casually by some hacky sci-fi writers, but I most certainly assure you it is real.
How does SpaceCore™ temporal shielding work? We project a localised distortion field around the time period or periods we want to project, and it shifts it out of space-time allignment by about 0.1 to 0.2 chronomicrons, preventing the enemy from arriving there in a stable state. Thankfully, we can project this field into the past without being physically present because, as you've already guessed, it is just a time machine projecting energy and not mass – that last one is the tricky stuff.
Now, members of the Council of Intergalactic Relations have tried to pass numerous laws banning time travel, limiting it to official scientific research and all that, however, as we've recently discovered it appears someone or something keeps going back in time and we've discovered that the laws have either not successfully been passed or someone keeps watering down the regulations, our first guess, is of course, the Hyluians.
Now, why don't we simply just keep sending our most advanced technology back in time? Well, as you know cadet, temporal spies are everywhere, and loose reverberators rupture containment fields, so the Hyluians often end up stealing our technology, as we do theirs.
Yes cadet, time is a tricky thing, but at SpaceCore™ we aim to make it simple.