Gawain wears the green girdle that was given to him by the Green Knight to show his shame. He shamefully lied to the Green Knight even though the knight knew the truth all along. Gawain is left to wear the girdle as a symbol of his shame.
Well 1) Hamlet is a prince 2) Not only is he a prince, but he is the prince of Denmark 3) Something tragic is going to happen because it's the Tragic History.