In Act 4, what are Claudius' defining character traits, and how might Hamlet respond to Claudius's statements?

In the fourth act, we see Claudius as a calculating man, who also seems to be losing himself to paranoia. He plans his Hamlet's death, aligns himself with Laertes, encourages a duel to the death.... a fixed duel to the death, and evades the reasons and facts behind Polonius' death. Hamlet is likely to respond in anger, and he will most certainly if hestitantly, accept the challenges set before him.