Does Each Instance Require Shared Resource?

Memory, in general, is not an issue because the amount needed is linear with the number of clients active. Also, we can use a factory if needed.
Sockets are not a problem because RMI re-uses sockets between two JVMs, even if different objects (thanks to RemoteRef).
The only possibility might be a log file, but then both choices would have to share one logfile.
Advantage: neither