A couple weeks ago I had a guy join my 2p blitz, take Caesar (since that was all that was left for him), and then abandon. I was upset but I can't really blame him since the best strategy for racking up XP is to abandon games in which you appear to be losing.
Start with a bad draw? Abandon! Move on. Why waste time when you're already down?
There is no skill-based rating system or else this would be much worse. But there is a rating system and leaderboards, and therefore incentive to maximize XP. As long as those are in place, there will be those who maximize any exploit.
There are many solutions but a simple idea is to lose XP for abandoning. [abandoner's level] x 100. This still allows for the occasional abandon when appropriate, but heavily punishes serial abusers.