Sophocles, a renowned ancient Greek playwright, did not write a specific play that combined a psychological murder mystery with a political thriller. This is what you've described. However, he is famous for his tragedies that explore complex psychological themes and societal issues. One of his most well-known plays is "Oedipus Rex," which incorporates irony and mystery.
In "Oedipus Rex," the protagonist, Oedipus, is determined to uncover the truth behind the murder of the previous Thebes king. As he relentlessly investigates the crime, he unwittingly discovers that he is the murderer he seeks. The play delves into themes of fate, free will, and the consequences of actions.
While not explicitly a political thriller, "Oedipus Rex" involves political intrigue as the search for the truth uncovers deep-seated secrets within the ruling family of Thebes. It also serves as a cautionary tale about hubris dangers and the limitations of human knowledge.
Although Sophocles may not have written a play specifically matching the description you provided, his works often explore psychological and moral complexities. This makes them timeless and relevant to various allegorical interpretations.