If marriage is a competition, how do you win?

My wife and her family are obcenely competitive and I am not. They see people as adversaries not as partners. Obviously this causes strain in our marriage as I'm trying to be a partner and my wife is trying to "be better" or whatever. I'm sort of introverted engineer/artist type so I don't really have a problem with it because I just ignore it. However, if I conciously tried to "win" our marriage competition, what does that mean and how do I win?