Recall the story of Alice and Bob, who like to be together but have different taste in movies. Each can choose to go to either Movie A or Movie B. For Alice, the payoff from going to Movie A is 3 if Bob is there and 1 if he is not. Alice’s payoff from going to Movie B is 2 if Bob is there and 0 if he is not. Bob’s payoff from going to A is 2 if Alice is there and 0 if she is not. Bob’s payoff from going to Movie B is 3 if Alice is there and 1 if she is not. Each is about to go to a movie. They forgot to settle on which one the last time they met. Bob has lost his cell phone, so they cannot contact each other.
A) Find a mixed strategy Nash equilibim in which each of them chooses to go his or her own favorite movie with some probability p between 0 and 1.
B) In the mixed strategy Nash equilibrium, what is the probability that they wind up at the same movie?