How do you deal with a "friend" who secretly dislikes you?

There is a "friend" of mine who invites me to her small parties, but not because she genuinely likes me. It's because she lacks close, true friends. She's done enough in the past to make me suspect that she really does not like me, or at least, does not trust me. She constantly tries to put me down in a public situation and never bothers to personally invite me, instead asking a mutual friend to deliver the message to me. She can't accept losing, even in games. I guess you can tell that I don't like her very much either. To the bystander though, I suppose we are friendly enough. She's also always trying to warm up to our mutual friends and draw them further away from me. How do I deal with this kind of "friend" (who uses very subtle methods) so that I don't cause a scene?