Wants to find out what is available and discover things first.
Socialiser
Wants to have fun, talking to people and doesn't really care about the game as an end to itself much.
Achiever
Wants to do as well as possible - as defined by the rules of the game. (Both written and unwritten)
Killer
Wants to do as well as posisble by their own criterion - usually breaking every unwritten rule. (And, to stereotype, all too many of them break as many written rules as possible too)
Bartle? is to blame for coming up with this taxonomy.
There are, of course, PersonalityTesters? for this sort of thing.