Based on this post, I thought it would be cool if you could train your character and pit them against another player's character. Or even yourself. What this could mean is that your PC would learn what you teach it (killing goombas, climbing ladder, fireballing incoming ducks). Then you could compete against that PC or your PC could compete against a friend or your PC could compete against your friend's PC.

I think this would bring online competition or cooperation to a new level. An interesting one at that.

Are you only talking about a deterministic course?

Reminds me of Umihara Kawase (a physics platformer)
with assited recording.

">Real person playing

I wasn't considering an determistic course. Actually I had Virtua Fighter 4 in mind when I was wrote that post. But I guess that would be a deterministic course as well.

I think this topic could be very hard to talk in the abstract, do you want to talk about a specific design and see how "AI training" "Competition" and "Cooperation" will all make perfect sense for the audience of the design?