I'm guessing that this prince isn't interested in her, but finds it convenient to be engaged to someone with a terrible reputation. He can use the fact she's known to be a bitch as an excuse to approach other women, and then he uses the fact that he's engaged so that he can dump the women he seduces as soon as he gets tired of them. Basically he's a scumbag, although he might be too self-centred to realise exactly what he's doing.