Why do you want to link identities to Bitcoin, because this would exclude a lot of people who would rather want to play this anonymously? I know it would be a great marketing tool to target specific individuals, but I still think Bitcoin Apps should protect people's privacy. You could still link people's phone numbers with the App, if you want to trace cheaters, but that should only be privileged information that should only be accessible to the game developer.
Let's not offer up our financial privacy, like people had to do with Ripple in the beginning. It will restrict your potential market. ^smile^
That's where the money comes from to get the money to the users. Business owners and contributors will likely want a certain demographic.
I don't necessarily want any names, just demographics that attract contributors to give away bitcoins.
Imagine a huge political rally happening in one location and someone puts out some bitcoins for all people who are libertarian leaning (based upon their Facebook likes and shares).
Or a new band with a certain style trying to get people to come watch them attracting people who enjoy their type of music.
Someone giving a presentation on home fire alarms might want to attract home owners.
Plus using Facebook, considering the distribution will be limited to a per person basis you can more easily weed out people who created a new account and only have a few fake friends. And you can give the option of posting on the person's wall "Jim Smith just made 50 millibitcoins on Bitcoin Chaser. Want to make bitcoins too? Click here.".