Shakespeare and Machiavelli

We know these two men for their incredible contributions to their own fields. Both of them are considered best by many; one in literature and other in politics. What interests me most is the similarity between their thinking in some matters. As we all know, Shakespeare had a very unique mind contributing to english language with thousands of new words including the names Jessica, Olivia, Imogen and Miranda. Machiavelli on the other hand is mostly known with "the prince" which I think is safe to say that caused a political revolution. The interesting part is similarities in ideas between Macbeth and The Prince. Machiavelli defends that a politician should appear to be good and actually be cunning and be prepared to act bad. Macbeth gains his throne by killing the good king Duncan. Shakespeare's idea of Macbeth's murdering Duncan and claiming the throne shows us that he actually shares the ideas of Machiavelli. To conclude, there are two points that should be considered. First one can reveal the origin where Shakespeare's political thoughts emerge from. James Shapiro argues that Shakespeare is influenced by Montaigne in writing most of his plays. If this is the case, Montaigne is a man who has acted as a mayor at some point of his life. I think that second point should be taken into account is how do these men with incredible minds see politics and politicians. Are they really vile creatures as described in " The Prince" and " Macbeth" ? If they are so; what does this tell us about lives ?