Many women seem to have a very firm belief that "men love the thrill of the chase." That is, men take great pleasure in pursuing a woman who is elusive. It strikes me now that I have never felt this, though I'm middle-aged, and have only heard of this from women. In a lifetime of knowing men and reading literature written by men, I have never once heard of, or run across a portrayal of, this supposed "thrill" from the inside.
Yet for all I know, there may be men who feel this. And even if men don't feel it, women may have reasons to work on this basis as a functional thing. That is, women may play hard to get and think that it works because "men love the thrill of the chase," though in fact it works for quite other reasons.
I would be glad to hear people's experience, and the gay perspective could be revealing too.