The three Fates are goddesses in Greek mythology, and even Zeus cannot disobey their dictates. These goddesses do not, however, appear as characters in this play.
Note that other gods were involved in the curse of the house of Atreus. Such curses are inescapable -- the curse is actually resolved in the ending of Oedipus at Colonus.
So often there is a tendency on the part of modern readers to interpret what they read in the context of more modern times. While writers such as Alexandre Dumas and Victor Hugo mention "fate," theirs is an interpretation of divine Providence. When other contemporary writers use the word fate, they may simply mean chance, or luck.
But, in the Greek theatre, Fate is a force in the universe; it is no character. To interpret this element or force as such is erroneous in the context of Oedipus Rex.
This seems to derive from the logical fallacy that what Fate throws at a person only serves to build that person into a stronger individual. A thesis against this position would encompass (1) an analysis of the logical fallacy and (2) proofs that speak against its truth, such as Jocasta's suicide and Oedipus's self-inflicted punishment.
"Who a person is, is what he becomes" might be another way of addressing the character/fate issue. Oedipus is, above all other things, a proud man; and it is his pride which determines and becomes his fate. In other words, if he had not been so arrogant, his fate might have been different. Hope that helps!
If we think of fate in this excellent play, I would be tempted to consider fate as a kind of external force against which the characters struggle and rage. I personally don't think of fate as a character in this sense. You might like to compare your impressions of fate in this play with the role of fate in Romeo and Juliet, which seems to perform a very similar role in the way that it represents a force that cannot be vanquished.
Fate can definitely be a character. Given that fate exists for many people as a concrete idea, one could not simply revoke its ability to be characterized. Fate, very easily, can be personified to possess characterizations which would enable "it" to walk and talk and be.
Fate can be a character, in a sense. If you think of Fate as having a will of its own, that things will be a certain way, Fate can intervene to make sure things happen the way it wants. In that sense, Fate is a character like any other.
Whatever the derivations we may get from the Freudian psychoanalysis of Oediupus Rex, if we probe deeper into the character of Oedipus we see him, at first, being driven from the very beginning by chances, prophecies or misdirections. But when comes the time for action, Oedipus always takes the decision that suits his character or as his character is. One may not call them all prudent or decisive, but his character decides his action. Ultimately when he decides to punish himself, that too is a reflection of his determined character's decisoin with regard to the action. Thus, Oedipus decides his own fate. Hence, is not that 'character is fate' and the vice versa? The concept is beyond the culpability of Oedipus or any one. For everyone: Fate is Character and Character is Fate.
am trying to say how you character is, is how your fate will be...
thanks but i meant it for Oedipus Rex by Sophocles