What characteristic do tragic heroes share?

We have two types of tragic heroes. The first type is the one by the ancient Greeks and Shakespeare in which the Tragic hero belongs to the upper strata of the society-normally a King or a Prince. He is basically a good person but falls due to his Hamartia - his tragic flaw which varies. In the modern definition by Arthur Miller, Tragiic hero can be any common man and he also has a tragic flaw. But in both cases, the tragic hero loses his battle against the cosmic forces, trying to retain his dignity and honour.