In the novel and film The Princess Bride, the villain Vizzini kidnaps the princess. In an attempt to rescue her, the hero, Westley, challenges Vizzini to a battle of wits. Consider this variation on the actual plot. (I do not want to reveal the actual story.) In the battle, Westley puts two identical glasses of wine behind his back, out of Vizzini's view, and adds iocane powder to only one glass. (Iocane is "odorless, tasteless, dissolves instantly in liquid, and is among the more deadly poisons known to man.") Westley decides which glass to put on a table in front of Vizzini and which to put on the table in front of himself. Then, with Westley's back turned so that he cannot observe Vizzini's move, Vizzini decides whether to switch the two glasses. Assume the two simultaneously drink all the wine in their respective wine glasses. Assume also that each player's payoff from drinking the poisoned wine is -3 and the payoff from drinking the safe wine is +1. Write the payoff matrix for this simultaneous-moves game. Specify the possible Nash equilibria. Is there a pure-strategy Nash equilibrium? Is there a mixed-strategy Nash equilibrium?