Question

1. 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. (LO1) a. Who are the players in this game? What are each player’s strategies? Construct a payoff matrix for the game. b. Does either player have a dominant strategy? If so, what? c. Is there an equilibrium? If so, what? Frank, Robert. Principles of Microeconomics (p. 259). McGraw-Hill Higher Education. Kindle Edition.

Answer 1

a: the players are you and your friend. No, there are no dominant strategies. Recall that a dominant strategy is one that yields a higher payoff regardless of the strategy chosen by the other player. In this game, if your friend plays one side, you will match that side; however, if you match, your friend will then want to change strategies, and you will therefore want to change your strategy in order to receive a higher payoff. No, there is no equilibrium. As discussed in part b, if your friend plays one side, you will match that side; however, ifyou match, your friend will then want to change strategies, and you will therefore want to change your strategy in order to receive a higher payoff

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