2. (This problem is inspired by Edgar Allen Poe's short story, \"The Purloined Letter\".) A blackmailer has stolen a letter, which, if revealed, would destroy the reputation of Lady S. She has asked Inspector Dupin to find that letter and destroy it. There are two places that the blackmailer could have hidden the letter. One place is easy to access, both for the blackmailer and for Dupin. The other is difficult for both of them. Dupin is allowed to look in only one of these places. The blackmailer has two strategies. Hide it in the easy place, Hide it in the hard place. Dupin has two strategies, Look in the e casy place, Look in the hard place. It costs Dupin 5 to look in the hard place and 0 to look in the easy place. If Dupin finds the letter, his payoff is 10 minus his cost of looking. If he doesn't find the letter his payoff is minus the cost of looking where he looked. It costs the blackmailer 4 to hide the letter in the hard place and 0 to look in the easy place. If Dupin finds the letter, the blackmailer's payoff is minus 10, minus his cost of hiding the object. If Dupin doesn't find the letter, the blackmailer's payoff is just minus his cost of hiding it. D) Find a mixed strategy Nash equilibrium for this game. E) In the mixed strategy Nash equilibrium, what is the probability that Dupin looks in the easy place and finds the letter? What is the probability that he looks in the hard place and finds the letter? What is the probability that he finds the letter