Egoism works in two philosophical aspects. Psychological and ethical/moral (there is a difference between ethical and moral but here I'm gonna use them interchangeably for simplicity) Egoism as a psychological stance argues that one is self-interest and everything one does is for that end. Moral/ethical egoism argues that one should act in their own self-interest. Egoists like myself use egoism in the political sense to argue that our institutions, religions, concepts of good and bad are merely "spooks of the mind." Simply put they are fixed concepts that only exist to hinder and impede our true nature and we ought to remove them from our behavior and thought process. Egoism in this interpreration therefore allows us to see it as compatible with anarchism because it also believes hierarchies such as the "spooks" are unjustified and should be dismantled.