Playing the campaign on Competent level, in one of the first shards, tiny.
The enemy AI is labeled as Skilled, which according to manual it is the opposite in the difficulty table (next to Overlord).

I have set up a trap using two Adventurer guards to make the enemy hero attack my home province and to catch him and kill him while on siege. I have noticed that AI revived the hero after roughly the same number of turns and he kept coming back over and over again. After the fifth or so resurrection, he came with two heroes.

It seems very unlikely for the AI playing by the rules to have enough money to keep reviving and buying a full army and even to purchase a second hero so soon, as the income from the several provinces he had owned would be insufficient, and raiding dungeons or exploring he was not, because he kept coming back at my border.

So he either started with a very large amount of money (not 500 as per the rules) or he receives free money according to some unknown rule.

Does anyone have an explanation for this?

They get some advantages, no maintenance for guards, and probably other stuff. But it is still possible to ruin them economically. They get a small amount of starting gold more than you (150 on expert). It gets a free alliance with the neutral factions, thats why they often quickly come with centaurs. They do have to pay to place guards, that is why they have empty provinces when they are broke.

I forgot most of the stuff, but there was a guy who made a hexeditor table so you could monitor the AIs values, watch them fight your guards and even take over their game. So you can find out what free stuff it gets.

http://www.gog.com/forum/eador_series/trainer_cheat_for_eador