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. Construct a payoff matrix for the game. Instructions: Note that if you get to keep the two pennies, this is a gain of one penny for you and a loss of one penny for your friend. So, your payoff would 1 and your friend's would be −1. Similarly, if your friend gets to keep the two pennies, then your payoff would −1 and your friend's would be 1. When entering the payoffs in the table below, use whole penny numbers (no decimals), and if you are entering any negative numbers be sure to include a negative sign (−) in front of those numbers. You Heads Tails Your Friend Heads for your friend for you for your friend for you Tails for your friend for you for your friend for you b. Does either player have a dominant strategy? . c. Is there an equilibrium?
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. Construct a payoff matrix for the game.
Instructions: Note that if you get to keep the two pennies, this is a gain of one penny for you and a loss of one penny for your friend. So, your payoff would 1 and your friend's would be −1. Similarly, if your friend gets to keep the two pennies, then your payoff would −1 and your friend's would be 1. When entering the payoffs in the table below, use whole penny numbers (no decimals), and if you are entering any negative numbers be sure to include a negative sign (−) in front of those numbers.
| You | |||
|---|---|---|---|
| Heads | Tails | ||
| Your Friend | Heads | for your friend for you |
for your friend for you |
| Tails | for your friend for you |
for your friend for you |
b. Does either player have a dominant strategy? .
c. Is there an equilibrium? .
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