I see the other answer just posted, but I think you are interactive with clients playing your game, so I may pose another approach (while BufferedReader is definitely valid in some cases).
If you wanted to... you could delegate the "registration" responsibility to the client. I.e. you would have a collection of connected users with a timestamp on the last message received from each... if a client times out, you would force a re-registration of the client, but that leads to the quote and idea below.
I have read that to actually determine whether or not a socket has been closed data must be written to the output stream and an exception must be caught. This seems like a really unclean way to handle this situation.
If your Java code did not close/disconnect the Socket, then how else would you be notified that the remote host closed your connection? Ultimately, your try/catch is doing roughly the same thing that a poller listening for events on the ACTUAL socket would be doing. Consider the following:
I think one of the features of the abstracted languages is that you are abstracted from the minutia. Think of the using keyword in C# (try/finally) for SqlConnection s or whatever... it's just the cost of doing business... I think that try/catch/finally is the accepted and necesary pattern for Socket use.