I like the idea (not that I'm in the dating market) but I think any purchase option is going to end up matching wealthy men with attractive women.

Instead, how about a different approach: You get say 10 stamps/day. There is no way to purchase them. Any message you receive can be replied to once with no cost. Also, the cost to send to someone is adjusted by the cost to send to you. (Another poster suggested ELO ratings, which makes sense.)

You have a choice between occasionally contacting the hot ones or fairly routinely contacting those at your level or below. It will make people much more realistic in who they choose to contact, taking long shots means not having any shot at the ones you might actually get.

The app should be tied to your identity (although I wouldn't require real name use in the prospect-facing side) so you can't just create a bunch of accounts to get extra stamps.