In the movie Princess Bride, the hero disguised as the pirate Westley is engaged in a game of wits with the villain Vizzini. Westley puts poison in either his own glass of wine or in Vizzini's glass. Vizzini will choose to drink from his own glass or from Westley's. Westley drinks from the glass Vizzini does not choose. (You should think of this as a game where players move simultaneously since Vizzini does not see which glass Westley has chosen).

a) Construct the payoff matrix for this game. Assume drinking the poison and dying gives a payoff of -10 and staying alive has a payoff of 10.

b) Does Vizzini have a dominant strategy? Does Westley have a dominant strategy?

c) Now suppose that Westley has another strategy which is not to put poison in any of the glasses, and this will give him a utility of a regardless of Vizzini's choice of strategy. For what values of a does Westley have a dominant strategy? Reconstruct a new payoff matrix.