Im sure Im not the only one that still gets invitations to play candy crush every now and then. Not sure if everyone knows this, but at its peak the game "candy crush" was generating 6 figures per day, due to how they saturated the market! Everyone was playing it, and it was because of this feature. It allowed them to spread like wildfire pretty much overnight!
Would it be possible to implement a feature that would allow them to share to their entire facebook friends lists the way those games do?
Unfortunately Facebook has changed a lot since then - and it's cutting down hard on these kind of "spammy practices". Unfortunately there is no way to implement something like this - while preventing that someone uses it for "bad practices". Trust me - we've had it before where a single user mis-used a feature like that... and Facebook then blocked the entire app for everyone out there (we were able to explain it and re-instate the app, but that functionality needed to be removed). Sorry :)