Inactive Recognized Developer
Well, if you want true peer-to-peer, you wouldn't be using any kind of hosting service at all. However, since most mobile operators firewall incoming connections to phones, and since the official APIs are very short on any kind of proper server socket (you can send or receive UDP broadcast, I think?) that would limit you to a mildly crippled WiFi-only network.
Even if you just want to use a central server for matchmaking and scorekeeping and such, you'll run into the same problems as above - you could find people across a larger range than WiFi, but you couldn't actually play with them. If having everybody connected to the same WiFi network is an unacceptable limitation, I'm not sure peer-to-peer is practical.
For something robust enough to handle actual multi-player gaming, I'd suggest going with a "cloud" provider (Azure, AWS, Rackspace, whatever). That doesn't cover the actual software, of course, but hopefully somebody else knows of a good solution there.