The problem is bigger than the above mentioned "perfectly similar units in 1-1 fight" tied-position. In standard fighting situations you don't want to move into striking range of your enemy, as then he gets the first strike and gets an advantage. At least in the public betas this has given a massive advantage to the human player. Really, the neatest solution is such that as often as possible, one player benefits more by standing back, because they have better ranged attack/spells. Give units ranged attacks, even if they are weak ones.
Another approach: make the initiative system slightly random ("+/-2 initiative each time it is checked"). This ensures that even if the initiatives of the units are the same, eventually one will get two moves in a row. This will be the time to strike.
If multiplayer will ever be in, this will be a real problem. If you get two stubborn players fighting each other, you will get a looong battle...
BTW about chess: I think it is real AI. Of course, the definition of AI is often such that anything a computer can do isn't AI. It is just statistics or brute forcing. Because that is what computers do...