Consider the following game, called matching pennies, which you are playing with a friend. Each of you has a penny hidden in your hand, facing either heads up or tails up (you know which way the one in your hand is facing). On the count of "three," you simultaneously show your pennies to each other. If the face-up side of your coin matches the face-up side of your friend's coin, you get to keep the two pennies. If the faces do not match, your friend gets to keep the pennies.

a. Who are the players in this game? What are each player's strategies? Construct a payoff matrix for the game.

b. Is there a dominant strategy? If so, what?

c. Is there an equilibrium? If so, what?