This happens to me on a regular basis at parties: for some reason or another, I find myself being one of the two guys talking to (gaming) the same girl at the same time. Girls absolutely love this.

I do not like giving them the satisfaction of being the prize, as it seems to put them on a pedestal, even if your game is full of negs and amused mastery. So usually I'll just find an excuse and go find someone else to talk to. However, a lot of the times the girl is the highest value girl available, so I have to settle with lower value girls. Worse yet, when I bump into her a while later, she's often still talking to the same other guy that was gaming her earlier.

Should you compete with the other guy? If so, how, (and how long)? Or should you settle with lower value girls?