I'm kind of old school and I think it is the man that chases the woman and not the other way around.
By wanting to be chased, a woman improves her perceived value. That's why she does it. The man won't think she's cheap and easy. Men wanting to win back an estranged wife need to do things to improve their perceived value, and chasing the woman doesn't do that.
You mention nice guys finish last. That sounds kind of dysfunctional to me.
Nice guys really do finish last. Part of the reason is dysfunctionality, where people can't appreciate niceness in others. Sometimes bad people feel bad (guilty) in the presence of nice people, so they don't like nice people. But, another part of it is that by being nice, someone might be coming up short in other areas. It's not dysfunctional to not appreciate someone who's niceness equates with being a doormat.