This is a question up to a fair amount of analytical debate. Like most tragic heroes in Greek plays, particularly in the Theban trilogy, the reader is left to guess at what parts of of Oedipus's eventual fate he is directly responsible for by way of free will and what parts are simply the cruel fate of the gods.
It is interesting to note that particularly in Oedipus Rex, the characters who suffered tragic ends were prophesied to meet these fates. By way of cause and effect, however, they only eventually did because they attempted to subvert these fates in the first place.
Laius was prophesied to bear a son that would kill him. Because of this, he left his son on a mountainside at birth. If it had not been for this, Oedipus would have grown up with his family and would have never been in a position where he met his father at a crossroads, at odds and unable to recognize him.
In the case of Oedipus, when he receives the prophecy about himself, the terrible deeds that seal his fate are already...
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