My take on why the game dynamics help Foursquare solve the problem of critical mass among one’s social network:
The bleeding edge users within any given social graph will normally encounter a scarcity of other users on any given social network. This makes said social network much less useful. Foursquare provides game dynamics that enable a single user value proposition—it does something for you even if you’re the only one on it.
Interestingly, in areas of high penetration of Foursquare usage, like New York City’s Union Square area, it has become extremely difficult to win any new mayorships for the most well-travelled venues. You basically have to go to certain places everyday to retain possession, and it’s nearly impossible to knock people off.
So why do people still use it?
The theory is that, in these geographic areas where political stability has been reached, there’s also a high likelihood that a lot of your friends are on Foursquare, too. (Unless you live in that cave under Union Square.) At that point, your reasons for using it become more social—finding out where your friends have gone to drink after work, meeting people for brunch, etc. I maintain that somehow, these forces—the ability to win new mayorships and the probability that enough of your friends are on Foursquare—are in balance with each other. When you find it really difficult to play the mayorship game, more of your friends are on it. For the one guy in Flathead Lake, Montana who is on it, he’s cleaning up like he was a Risk World Champion. That will slow down right around the time the rest of his friends catch up with him and join. So far, that’s been timed pretty well. I’ve seen very few people join Foursquare and never use it, unlike Twitter.