You could use "determined" instead of "desperate" and then suddenly it sounds like a value proposition again.

If you assume there are plenty of suitors, then playing hard to get would advertise yourself to the folks on the higher end of the desirability curve, possibly giving you more selection there, and having reasonable fallbacks otherwise.

If there aren't a lot of suitors, then you'd probably want to go for the best you can get, because there's probably not much better, but almost certainly worse.

I wonder if there's a good way to formally analyze this

Nobody is forcing you to select from your desperate suitors. Having many suitors means you have options and are free to casually pursue your own interests and the queue of suitors is there to validate your high status in the eyes of the interest you are pursuing.

That depends entirely on how hard you play and when you allow yourself to get got. The article points this out. You've got to make the other person think you're just out of reach but maybe if they stretch . . .

It's basically flirting but longer?