There's something frustrating about being asked to "name my price" before I've played the game: I know that I'll have a much better knowledge of how much the game was worth to me after I've played it. I really want to pay the fairest price I can, but it's impossible for me to know what that would be before downloading! Stop asking me to guess! I wont! And there's no need.
Paying nothing and then paying again later isn't a very clean solution, it wont occur to most people, and by the time I get around to finishing a game, I will have often forgotten whether I've paid, I might not get around to it.
Solution: Provide a way to tell the site to remind us after a bit, or keep a list of our "To pay later" purchases that we can check every now and then.