When Polonius arrives in scene 2, act 1, Hamlet begins behaving with the mentality that he displayed earlier in the play, as being a bit loopy. He has become fascinated with the sudden appearance of the actors, So I cannot help but wonder if it this that has made him behave bizarrely, or weather he is doing it because Polonius is here.

However, Hamlet also mentions that he will contribute to a scene in the play, where he will inset a scene of murder, similar to how Cluadious murdered his farther, and will see how he re-acts ('I'll observe his looks'). This way, if Claudius displays signs of distress, Hamlet will think that he will finally have evidence of what Claudius did to his farther and be bale to protest against him - something he was reluctant to do earlier because he had no evidence. Because of this, I think Hamlet is starting to appear as quite a clever character, and his loopy behaviour is starting to disguise this well, as Polonius thinks that he may be generally loopy and has reported this to Claudius.