If we are meant to answer your question based upon Aristotle's definition of a tragedy and tragic hero as described in his Poetics, then Oedipus must be the engineer of his own downfall. A downfall that has been created by the hero himself is an important component in a Tragedy, according to Aristotle, as it inspires great fear and pity in the audience. The audience can see the role that the hero's nature, his tragic flaw, has played in his demise, and sensing the inherent humanness of this, they empathize with the hero. For Oedipus, the tragic flaw is his own hubris -- his belief that he can outwit the gods and beat the oracles at their own game.
Oedipus learns, when he is growing up, that there is an oracle that he will kill his father and marry his mother. To escape this fate, he flees his home (which he does not realize is not the home of his birth, but his adopted home) and travels far away. During his trip, he meets a man on a narrow road. Neither of them will budge. In a fit of rage, Oedipus kills the man, who turns out to be King Laius of Thebes, though he does not know it at the time. He also solves a riddle and saves Thebes from a plague. In reward for this, he marries Laius' widow, Jocasta.
Well, it only takes the course of the play for Oedipus to discover that he could not outwit the gods. He did in fact, murder his real father (Laius) and marry his true mother (Jocasta), all as he was running away from the man and woman he believed were his mother and father. It was his tragic flaw, hubris, that caused him to attempt to outwit the gods, and it also makes him a tragic hero.
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