So we can conclude that this is just some sort of AI trait? I think that's probably the best conclusion we can come to.
I was going wide that game, so perhaps it was just that I grabbed some land they wanted. Probably just mad I was able to grab land before them.
Yeah, that's probably it. Both Alexander and Caesar are really expansionist, and Alexander is super aggressive, and will declare war on you if he think it can benefit his empire. Some civs won't declare war unless they hate you, some civs will declare war if other civs ask them to do so (and you can use this to your advantage by bribing civs to declare war with each other), but other civs will just declare war because you exist and you have land that they want. I wouldn't call any of these reasons 'no reason', but different civs will declare war for different reasons, and eventually you kind of feel out what these are.
On the AI accepting peace; I had a pretty big army and out-teched Rome. But Rome still wouldn't accept peace no matter what.
I find that in this game, the AI won't accept peace until you almost take one of their cities. No matter how big your army is.
But yeah, I definitely agree, it's probably just the way Alexander and Augustus are programmed.
I did another wide game with Germany and never got DoW'd. I was even a warmonger and was able to befriend Siam the whole game.
Here's probably what happened based on what you've told me.
Alexander hates you and wants your land, because he hates everyone and wants everyone's land, but you're close by. He visits Rome with an offer.
Alexander: "CivAddict is a threat to the stability of this world, and can only be dealt with through war. Will you join me, friend?"
Caesar: "Yes, let's get this started."
Then, you go and crush Rome's army and have a better army than them. Unfortunately, you crush them too quickly, and Rome is forbidden by the game itself from making peace with you for a little while because they've made a deal to be at war with you with another player. Therefore, make peace isn't even presented as an option for you. Eventually this deal expires, but you associate this with where you are in the war, when in reality it's just x amount of turns from the declaration that they are willing to negotiate (forget exact number). If it was presented as an option and they wanted everything you owned, then that's different and because the game overvalues number of units and undervalues technology in calculating combat strength.
Just by the way, if I'm wrong and Alex isn't close by to you, this could easily be Caesar asking Alex to help him instead. Wouldn't really change anything in the way it worked.