In Antigone, Sophocles introduces us to the first great feminist hero, Antigone. She is outspoken against a man, the King. In terms of psychoanalysis, Antigone follows the gods laws (superego) and not the need for revenge (id), thereby exposing Creon's self-serving behavior. In terms of Marxist theory, Antigone is a hero to the proles because refuses to marry the prince and live a life of luxury. Not only that, but she chooses to defy martial law and bury her brother, knowing that she would receive the death penalty. Her existential predicament, though, is whether or not to commit suicide. Rather than have her fate determined for her, she determines her own.
In Oedipus, we have the proletariat suffering from the sins of the bourgeoisie (Marxism): the plague upon the children is brought upon them by the incest and regicide of the Royal House of Thebes. Unlike Antigone, we have Queen Jocasta who follows the patriarchal order to protect her status: she is in denial of the truth and freedom. She, therefore, goes against the ideals of feminism and Marxism. However, Joacasta, is in the same existential predicament, for she commits suicide, not to escape public execution, but because of shame. She, therefore, is no existential hero either. Oedipus is the existential hero: he refuses to kill himself; instead, he punishes himself and suffers the responsibility of knowing the truth.