While there are clear differences between Death of a Salesman by Arthur Miller and Oedipus Rex or Oedipus the King by Sophocles, there are also important similarities. The most important similarity, it would seem, is the inability of the protagonists to really “see” what is occurring around them and within their families. Both characters, who are the head of their respective families (and Oedipus of his kingdom), are blind to how their actions harm the others. In the case of Oedipus, the inability to see is taken to an extreme at the conclusion of the play when the title character horrifically gouges out his own eyes.

Yet, even before the climax, the theme of blindness is present is Oedipus Rex as it is in Death of a Salesman. Oedipus searches for the murderer of the previous king (his own father) and is blind to the fact that it was he who killed him and who has therefore fulfilled the prophecy that has brought such difficulty to his kingdom. In Death of a Salesman, Willy Loman is blind to how his constant dissatisfaction with his son Biff and his inability to see any good in Biff’s life is hurting Biff and his entire family.

In both stories, the title character seems to take pride in what they themselves do. Oedipus is proud to have become the king of Thebes. Willy says that he is proud to be a salesman. Yet, in a sense, it is false pride in both cases. Willy is struggling as a salesman. Oedipus has not attained the kingship in the traditional manner and is also struggling under the weight of the plague that he unknowingly unleashed on his people.

Moreover, perhaps the most significant similarity between the two plays is that neither character really knows him. Willy continues to bluster about how he could have done well if the owner’s father were still running the company. Oedipus does not recognize that he is the cause of the plague.

Willy Loman and Oedipus are both tragically blind to how they are destroying their families, and in Oedipus's case, his community, which has developed a plague due to his actions. Both arguably are blinded by pride; Oedipus is unable to see that he is the cause of all the problems, and Willy stubborn refuses to abandon his false conviction that he will make easy money and find popularity and financial success as a salesman. Willy is blind to and perhaps ashamed of the fact he would have done better and been happier working with his hands. Both plays also employ dramatic irony, a technique in which the audience knows more than the characters. Audiences in Greece knew the story of Oedipus before they entered the theater, and Miller, in Death of a Salesman, uses staging and conversations characters have when Willy is not present to communicate to the audience more than Willy knows.

Willy's false conviction that you do not have to study, work hard, or know things because success is all a matter of having friends and a winning personality derails his sons's futures, as does his recklessness in having an affair, which, unbeknownst to him, disillusions his son Biff profoundly. This blindness to reality also hurts his wife, who has to live from paycheck to paycheck as they buy goods on credit while awaiting the big success that never comes. She also worries about her husband's increasing divorce from reality. In the end, Willy's only chance to help his family is suicide.

Oedipus, unbeknownst to himself, murders his father and marries his mother. This information rips apart his family when revealed, causing his mother's death by suicide and Oedipus to blind himself. 

Both are family tragedies but with wider implications that prod us to think about our false ideas and blind spots.

A number of ideas connect these two plays. From similar protagonists and supporting characters to actual events in each play, the works of Miller and Sophocles offer a rich set of comparative elements. The most significant similarities are found in the protagonists. 

The protagonists are characterized by a fundamental distance from factual reality. Willy Loman is delusional and incoherent. He hallucinates. Importantly, he is also dedicated to a certain illusory vision of success and achievement that has buffered his relationship to reality for quite some time. 

Many critics have asserted that Willy is a modern tragic hero, and that his tragedy lies in his belief in an illusory American Dream.

Oedipus, a quintessential tragic hero, is also buffered from reality. He believes in a set of facts that are proven false as the truth of his situation is revealed over the course of the play. This false relationship to reality presents a significant similarity between the characters of Willy Loman and Oedipus.

Taking this point a bit further, we also see both Willy Loman and Oedipus actively struggling against what they perceive to be their fate. Oedipus energetically rejects the prophecy that has inevitably shaped his life.

...Oedipus struggles against the oracle that predicts his hand in his father's death and boldly asserts that it is wrong...

Willy Loman sees himself dying as a failure. To avoid such a fate, he commits suicide.

Self-inflicted harm occurs at the climax of each play. Oedipus blinds himself and Willy commits suicide. Both acts of violence are undertaken as a means to assuage and recompense wrong-doing and guilt over a failure to do "the right thing". 

Female characters in both plays act as a voice of reason and restraint, advising the protagonist to take stock of the value of his life. Linda and Jocasta each attempt to persuade their husbands to abandon their quests, anticipating the tragic outcome of any continued pursuit.