Balance Issue, but good
Getting the lvl 3 cooldown is too imbalanced. After getting that, all I had to do was spam one unit and they'd eventually manage to hit the enemy base and nuke its hp down to zero.
Make that either more expensive, or more counter-able. Considering the computers never get the 0.5s cooldown (or at least for as long as I was playing it..) it becomes a completely unfair advantage that no matter how upgraded their units become, you can beat them down with sheer numbers. This also breaks the RPS system you've put into place, as I can just simple spam more units which will eventually overcome *any* obstacle.
Interesting concept, though, and I like the implementation.