The problem and confusion with this term is that you call the utility function “selfish” even when the agent cares about nothing except helping others. I think this is about the only reason people complain about this terminology or misinterpret you, thinking that whatever concept you mean by this term should somehow exclude helping others from terminal values.
By “selfish utility function” I mean exactly the same as “private utility function”. I mean that it is that agent’s utility function.
The problem and confusion with this term is that you call the utility function “selfish” even when the agent cares about nothing except helping others. I think this is about the only reason people complain about this terminology or misinterpret you, thinking that whatever concept you mean by this term should somehow exclude helping others from terminal values.