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Distance - the intervening mountain range, swamp, or near barren grasslands make logistics of open war extremely impractical

Attitude - it just isn't worth the trouble unless they bother us first

Internal politics - cold wars can be more about how the ruling class uses them to influence their own people than external politics. Maybe the distrust is mostly or entirely an excuse to say things like "pay your taxes or the dragons will get us!"

Excessive cost - alternatively, the border is close and boiling with tensions, but the empire is scared about massive loss of life from dragons (which would qualify individually as weapons of mass destruction, easily), whereas the dragons are concerned about the risk of losing even one of their few number of true dragons in open war.

One means to keeping a cold war going is the two antagonistic sides having the means of mutually assured destruction. These two empires could go to full out war with each, but in the end at best, one side will win. At worst, continued stale mate. With an "unlimited" supply of cheap soldiers (the serfs on the human side and humans on the dragon side) wars would break out often as the elites did not truly feel the consequences.

Now if both sides new that full out war would guarantee their societies utter destruction, they would sit in a cold war status, jockeying for dominance in other arenas, to better their positions.

No better example of how to keep a cold war going than the events from 1950's to 1988. One side just ended up collapsing because it could not keep up with the other.

One way would be to introduce a third party. It's neutral towards both the dragons and the knights, and it wouldn't stand a chance if it went to war with either of them.

But if both the dragons and the knights believe this third party could easily overrun them if they went to war, even if they are the winners, that would be a strong motive not go to war. Note that this third party doesn't actually have to be strong enough, or even have the desire to war -- all what needs to happen is that the dragons and knights believe they'll lose out to the third party once they defeat the dragons/knights, as any war between them will mean heavy losses on both sides.

Mutually Assured Destruction

Yes, it worked for Earth, it should work for your world.

The main difference is that the means for destruction are asymmetric in your case.

I'll assume for the question that both sides have significant defenses against each other's armies and capabilities, so that a conventional military strike at any vital point is unlikely to succeed.

The dragons could however launch a series of night raids to literally scorch the earth, burning the humans fields, orchards and lightly guarded livestock. This would destroy an entire harvest and plunge the humans into famine that will bring the empire down. There just aren't enough skilled soldiers to defend effectively against this. A handful of militia archers at each village is not going to make a difference to this.

The inability to destroy the food supply during winter (when it is in well-defended storage buildings) is not critical as winter is terrible for warfare anyway. With limited mobility and supplies, an attacking human army would be easy prey for the dragons, whose flight gives them the power to strike anywhere.

The sorcerers have some devastating magic ritual they could perform that would seriously harm, but not disable the dragons. Perhaps they could make human women infertile to dragons or kill all the dragon bloods. This would disrupt the social order of the dragons and probably a rebellion by their human subjects if the dragonbloods die.

Both attacks leave the other side able to retaliate and no reason to hold back. Both would also require extensive development to protect against, which would be visible and risk triggering a pre-emptive attack. This way the war stays cold.

Cold War

Magic when used on a large scale could have the side effect of drawing heat from the world. Maybe this is how magic works, or it could just be an accidental byproduct; either works. An all-out war would result in the mass deployment of weaponised magic by both sides, and plunge the world into a new ice age that directly kills off large swathes of the population and destroys both kingdoms' economic base. Presumably both sides found this out the hard way, when hostilities were abruptly cancelled by an unexpected winter.

The cold war between west and soviets was never full blown hot war - it came as result of defeating a common enemy and divvying up the spoils of that war. You could just basically copy that as the origin for why they even share a border in the first place.

Have the current situation be the result of being former allies who destroyed a kingdom in the middle - kingdom of lizard people or whatever, that's not important - just make them be so horrible that neither side wants to appear as being as horrible as they were and so mass executions, burnt ground tactics and such are not viewed favorably by either side - also you could have there be other semi-independent city-states scattered on the border between the two build on the ashes of the lizard people who would be totally extinct now - or at least thought to be. Then the two cold war sides would try to influence those states to join them and not the other side, they would fund shadow wars and provide military assistance and such, but stay technically out of it. Both sides would have to be engaged in this - Both sides would posses weaponry/army to wipe out any city in the middle grounds too, but will rarely do full invasions or attempts at such and in case another side does one, the resistance is not supported openly by the other.

You could also just make the magical powers be dependent on the distance to some magical object or home temple, further making it less feasible to attack either side full blown, so instead proxy skirmishes are done on the states that live between the two.

I mean, you already basically could just label the Dragons as the red menace. That kolkhoz peons basically have no rights whatsoever just underlines that and that there are special people who have more rights(communist party members or dragonkin, who can get rid of common folk at will) - and that passports are easily acquired and can be used to move between states in the west but not so easily into the border states or for moving from one major block to another.

Give them personal reasons to hate each other, but political reasons to avoid conflict.

Fights between parities ("wars") are, generally speaking, fought over limited resources - whether that's iron, water, or grazing land, one country has something the other country wants so they invade. So just make it so that the two countries use entirely different resources, and have no interest in the others land. At the same time, give them some sort of personal benefit - for instance, any time a dragon eats a sorcerer or a sorcerer kills a dragon, they get stronger.

That gives them incentive to keep the war going (because they want it to be socially acceptable to kill each other), but at the same time keeps it from getting hot - because wars are expensive for everyone, not just the frontline combatants, and they don't want to be paying out money to fund a war that will give someone else the benefit.

With this set up, you get lots of rhetoric about how much each side hates each other, riling up the population, followed by raids of a single individual with a small band of helpers to hunt down one of their opposite number, but no large scale fights.

Peace is impossible, because individuals are not going to stop the hunting and killing, not when they get so much benefit from it. A full blown war however would be disastrous for the emperor, because it will cripple him economically, while dramatically boosting the power of his nobles - almost certainly resulting in a coup. Therefore, cold war!

To answer the question

What ways might I keep these two empires from trying to start a war with each other?

Put a third party in it, which threatens to annihilate both dragons AND humans.

Much like the elves and dwarves of Lord of the rings, both of them has a huge grudge on each other, yet they allied during the attack of the orcs in the movie Battle of the Five armies. Heck, some elves where killed by the dwarves too.

The Question I found myself asking is: "What is the motivation for not destroying the other party?"

The mutually assured destruction aspect was already mentioned by other posters, so I'll skip this.

Another reason a party won't go to war could be that they don't have the troops to succeed. The dragons could think that the human magic is enough to destroy them while in reality the humans are very sure that they'll be wiped in a full out war, keeping up the illusion of power through magic, planned misinformation and other trickery. (Russia used to have inflatible tanks to trick satellite spionage)

Also, the humans could also have taken dragon eggs hostage. Direct descendants of the queen/empress. Their magic used to keep the eggs in a stasis where they neither hatch nor die.

The dragons may fear an uprising of half-dragons and humans, unsure if the magical abilities of their slaves and underlings may be enough to start a dangerous revolution.

As dwllama mentioned, cost is a very important factor of war. Troops, supporting the society and morale of citizens.

Hope this helps you.

How did the real cold war stay cold?

With the fear of nuclear weapons.

As mentioned before me, mutually assured destruction is a wonderful reason for this, and will be most convincing to readers, as it has real precedent.

You should think in advance if you eventually want the war to turn hot. At that point you either have to

a) Make someone disregard the mutually assured destruction.

or

b) Make something change so that m.a.d. no longer applies.

a) has the problem that then the whole world is inevitably screwed and the story you can tell from that point onwards is constrained by the fact that everyone is dead.

b) is better (in my opinion) since it constrains you less. However this must be carefully crafted. I don't want to write your story for you but I'd probably create some rare tools or artifacts that can be used to inflict unimaginable destruction and horrors, but which somehow grow old and are discovered to have lost their power over time...

Humans constantly improve warfighting skills. Dragons don't.

Humans use tools to fight. And since they are the very definition of an arms race, the tools get better every year.

Whereas dragons mainly fight with their God-given sharp and burny parts, and don't arms-race with silly gadgets.

Just at extremes, a dragon would be able to achieve a total wipe-out of a first-string Roman legion. But a modern junior-varsity force, such as Estonia's army with its MAPATs, Javelins and radar-guided AA guns... or Turkey's G-class frigates with SM-1MR missiles, could exterminate the dragons by pushing buttons.

All this to say, it is inevitable that there'll be a point where the knights are able to hit the dragons hard enough to make the dragons think twice. That is not yet license to kill dragons; a dragon fight would still exact a heavy toll, and of course the knights remain totally vulnerable to countervalue damage e.g. against undefended villages. So either party will pay a heavy price for fighting.

At that point, each side could destroy the other, but the price they'd pay is not worth it. Neither side would have any opportunity for a debilitating "first strike" as would occur in nuclear war, as the knights are too dispersed, and the dragons are too many.

The knights may have reached a "live and let live" philosophy of "no reason to attack the dragons if they aren't attacking us". The dragons clearly have that philosophy already, since humans survived the period when the dragons could crush them.

Against this balance of terror, you also have trade. If knights and dragons have cause or ability to do business with each other, nothing stops war like trade. That's a big part of why America has so many trade agreements.

Every feudal state, ever: "The knight sorcerers rule a feudal state."

England, Spain, France, etc. : "The dragons are ruled by a dragon empress and her family"

Jews, aka : "Female dragons don't own lands; they tend to hold positions like alliance brokers, priestesses, spymasters and scientists."

I don't see how this can be a cold war because as written, the dragons could destroy the world if they wanted to but it doesn't sound like humans can. There would need to be a case of mutually assured commerce. And it sounds like the 'female dragons' have that covered just like they always do.