RMI is a very high latency, high level protocol, and it's totally unsuitable for realtime. For fixed turnbased games it'd be ideal, as these are very like the normal business software client/server model.
You could sensibly use RMI for your lobby server though to manage setting up games and logging in / out.
However your realtime protocol will have to be TCP/IP or UDP/IP sockets. With <20 clients you can probably get away with using normal sockets and IO, although you might want to investigate using the new javax.nio package for maximum performance.
Depending just how realtime you need the game, you might have to axe TCP/IP and go for UDP, which involves writing your own TCP-like protocol over UDP. It's not particularly hard but not particularly easy either.
Cas
