Egocentric at 6? You betcha!
You said she was a quiet one? Sometimes kids 'overcorrect' when they are changing their behavior. It also may be she is failing to notice her peers' social
cues because she lost in her own world. Instead of discussing the 'shoulds' of empathy (which will likely make her defensive), appeal to her logical side. Social rules are tricky, subtle, and extremely varied. Help her become a detective of these. Most young kids don't usually feel empathy with their friends, they've just learned the social rule of sharing, compromising, etc. This implies empathy...which makes adults happy. Help her 'fake it til she makes it'. Even if she never fully makes it, social behavior is more about following the rules than feeling them. Before play dates, try giving her secret missions to carry out (ie play a game her friend wants, letting her friend go first, etc). Reward her later for mission complete.
