Suppose two friends, Rick and Susan, want to go to a movie. The movie tickets cost $10 each. They decide to play a game of Morra to decide who will pay for the tickets. In this game, they hold out one or two fingers simultaneously. Susan wins if the fingers they both hold out add up to an odd number, and Rick wins if they add up to an even number. Susan pays $20 to Rick if she loses, and receives $20 from Rick if she wins.
a. Construct the pay-off matrix for the game. Is this a zero-sum game? Why or why not?
b. Is there a pure strategy Nash equilibrium in this game? Explain your answer.