Suppose that you and a friend play a "matching pennies" game in which each of you uncovers a penny. If both pennies show heads or both show tails, you keep both. If one shows heads and the other shows tails, your friend keeps them.

(a) Show the payoff matrix for this game.

(b) Solve for the pure-strategy Nash equilibrium for this game, or show that one does not exist.

(c) Does this game have a mixed-strategy Nash equilibrium? If so, what is it