By "selfish" I mean how each human (apparently) cares about himself more than others, which needs an explanation because there can't be a description of himself embedded in his brain at birth.
Pointing at self is possible, which looks like a reasonable description of self, referring to all the details of a particular person. That is, interpretation of individual's goal representation depends on the fact that the valued individual is collocated with the individual-as-agent.
Just as how a file offset value stored in memory of my computer won't be referring to the same data if used on (moved to) your computer that has different files; its usefulness depends on the fact that it's kept on the same computer; and it will continue to refer to same data if we move the whole computer around.
No, that's not the meaning I had in mind.
Now I'm confused again, as I don't see how these senses (one I suggested and one you explained in parent comment) differ, other than on the point of caring vs. not caring about counterfactual versions of same individual. You said, "each human (apparently) cares about himself more than others, which needs an explanation", and it reads to me as asking how can humans have the individual-focused utility I suggested, that you then characterized as not the meaning you had in mind...
Human values seem to be at least partly selfish. While it would probably be a bad idea to build AIs that are selfish, ideas from AI design can perhaps shed some light on the nature of selfishness, which we need to understand if we are to understand human values. (How does selfishness work in a decision theoretic sense? Do humans actually have selfish values?) Current theory suggest 3 possible ways to design a selfish agent:
Note that 1 and 3 are not reflectively consistent (they both refuse to pay the Counterfactual Mugger), and 2 is not applicable to humans (since we are not born with detailed descriptions of ourselves embedded in our brains). Still, it seems plausible that humans do have selfish values, either because we are type 1 or type 3 agents, or because we were type 1 or type 3 agents at some time in the past, but have since self-modified into type 2 agents.
But things aren't quite that simple. According to our current theories, an AI would judge its decision theory using that decision theory itself, and self-modify if it was found wanting under its own judgement. But humans do not actually work that way. Instead, we judge ourselves using something mysterious called "normativity" or "philosophy". For example, a type 3 AI would just decide that its current values can be maximized by changing into a type 2 agent with a static copy of those values, but a human could perhaps think that changing values in response to observations is a mistake, and they ought to fix that mistake by rewinding their values back to before they were changed. Note that if you rewind your values all the way back to before you made the first observation, you're no longer selfish.
So, should we freeze our selfish values, or rewind our values, or maybe even keep our "irrational" decision theory (which could perhaps be justified by saying that we intrinsically value having a decision theory that isn't too alien)? I don't know what conclusions to draw from this line of thought, except that on close inspection, selfishness may offer just as many difficult philosophical problems as altruism.