"Psychopaths" or "sociopaths," which are just colloquialisms for folks with antisocial personality disorder, are not capable of experiencing or expressing empathy. They care deeply about their own experience, however. There are good stuides showing that the brains of these people do not fire when they are shown images of other people experiencing suffering or pain. When imagining themsleves in pain or suffering, their brains fire like mad, illustrating the fundamental issue, which is that they are able to experience "empathy" reallly only for themselves.