To what extent does Arthur Miller make you feel that Eddie was responsible for his own death?

In A View From the Bridge Arthur Miller shows Eddie Carbone as being very much the architect of his own downfall. His obsessive, unhealthy feelings toward his niece Catherine drive him toward making a series of bad choices that ultimately lead to his death.
Eddie is so insanely jealous that he sets out to get his wife's illegal immigrant cousins, Marco and Rodolpho, deported back to Italy. Catherine's been growing closer to Rodolpho and Eddie just can't handle it. So in a fit of spite and desperation, he rats out his wife's cousins to the authorities. This way he hopes to get Rodolpho out of Catherine's life, leaving the field clear for himself. Unfortunately for Eddie, this fateful decision backfires badly. Not only is he ostracized by the local community for informing on the two Italian immigrants, but he ends up being stabbed to death by an angry, vengeful Marco.