I have only recently come across an article by Maurice Pope former Professor at Capetown University (though it was published in Greece and Rome in October 1991). It contains ideas vital for the understanding of the play Oedipus Tyrannos (as Sophocles called it - Rex is, as we'll see, a poor translation of tyrannos into Latin, as poor as Oedipus the King is into English).
Sophocles never actually calls either Oedipus or Laius "king" (Greek basileus), but this has not deterred translators (whether into English or French) from making him a royal - and also upgrading everything associated with him. Thus Jocasta, his wife, is promoted to queen (basileia is never used by Sophocles), his chair becomes a throne, his house becomes a palace and his stick becomes a sceptre. A basileus is a hereditary monarch, with special status (like our own dear Queen, Elizabeth II, or Henry VIII) - Oedipus was an ordinary man who was elected leader of Thebes: perhaps "Oedipus the President" would give a better indication of his status. The word tyrannos is nicely ambiguous in Greek: most Athenians would have pictures a tyrant in what's become the traditional meaning: a self-appointed ruler with military backing who is cruel, selfish and abuses his citizens, especially women (see Plato Republic Book 8). (Does this sound like any Presidents we know?) But there's no other word in Greek for a well-meaning ruler who rules alone: certainly not basileus or king. Thus. I believe, Sophocles intends to categorize Oedipus: a man appointed for life, to do a job, and taking it seriously. (John Ferguson wanted him called "Oedipus the Dictator": is this better or worse than Oedipus the King?)
Pope also solves one of the other small but puzzling problems of the play: that of Creon's apparent "power-sharing" (where he says he wouldn't have wanted to be tyrannos as he had enough power already). But this confuses power - arche (which Oedipus alone exercises), with status - kratos (which Creon has as brother-in-law to the tyrannos). This in his defence is the true meaning of the Greek sentence translated by Fagles (following all other translators!): :
I'm not the man to yearn for kingship,
not with a king's power in my hands
This absurd statement becomes intelligible, once we remove the idea of "kingship". The Greek means "I personally have no desire to be a tyrant, any more than I want to behave like one." Creon distances himself from the role of the tyrant, which he does not aspire to - nor would any sane man. He prefers his own modest station to that of the tyrant with all its temptations and risks.
Now, perhaps, we can appreciate one more of the ironies of the tragedy: when the man who was tyrannos turns out to have been basileus all along - having unwittingly taken on the position of hereditary monarch!