I had an encounter yesterday where a guy asked me if I wanted to battle.
I asked what level he was at, and he said 13. I was level 10 with my four pokemon and didn't even have the first badge yet but I was like "Sure, let me go heal up."
So we battled and he was doing pretty well but then I took out his Charmander and then I assume he just got a couple of others not as high level and almost immediately after I beat his Charmander, the battle was aborted and my opponent had "disconnected".