Question

1. Alejandra, Brittany, and Cho, are going to their high school prom and are picking out dresses to wear. Each girl has the same selection of dresses, and chooses between a Red dress, a Blue dress, and a Green dress. The competition for prom queen is competitive, and so each girl wants to stand out from the other girls. However, each girl also has their own preferences with regards to the dress she likes the most. If a girl gets her most preferred dress and is alone in wearing that dress, she gets a payoff of 3. If a girl gets her second preferred dress and is alone in wearing it, she gets a payoff of 2. Wearing her least preferred dress, but being the only one to do so earns her a payoff of 1. If two girls are wearing the same dress, they both get their payoff of being alone in the dress minus 1. If all 3 girls are wearing the same dress, they all get -3 to their payoff. Alejandra prefers Red to Blue and prefers Blue to Green. Brittany prefers Blue to Red and Red to Green. Cho prefers Green to Red and Red to Blue. (Example: If A and B are wearing Red and C is wearing blue, A will get a payoff of $3 - 1 = 2$, B will get a payoff of $2 - 1 = 1$, and C will get a payoff of $1 - 0 = 1$.) (20) (a) (15) Write down the game in strategic form. (b) (5) What are the pure strategy Nash Equilibria of the game? Underline the Best Responses in the game above.

          1. Alejandra, Brittany, and Cho, are going to their high school prom and are picking out
dresses to wear. Each girl has the same selection of dresses, and chooses between a Red
dress, a Blue dress, and a Green dress. The competition for prom queen is competitive,
and so each girl wants to stand out from the other girls. However, each girl also has
their own preferences with regards to the dress she likes the most. If a girl gets her
most preferred dress and is alone in wearing that dress, she gets a payoff of 3. If a
girl gets her second preferred dress and is alone in wearing it, she gets a payoff of 2.
Wearing her least preferred dress, but being the only one to do so earns her a payoff
of 1. If two girls are wearing the same dress, they both get their payoff of being alone
in the dress minus 1. If all 3 girls are wearing the same dress, they all get -3 to their
payoff.
Alejandra prefers Red to Blue and prefers Blue to Green. Brittany prefers Blue to Red
and Red to Green. Cho prefers Green to Red and Red to Blue. (Example: If A and B
are wearing Red and C is wearing blue, A will get a payoff of $3 - 1 = 2$, B will get a
payoff of $2 - 1 = 1$, and C will get a payoff of $1 - 0 = 1$.) (20)
(a) (15) Write down the game in strategic form.
(b) (5) What are the pure strategy Nash Equilibria of the game? Underline the Best
Responses in the game above.

1. Alejandra, Brittany, and Cho, are going to their high school prom and are picking out
dresses to wear. Each girl has the same selection of dresses, and chooses between a Red
dress, a Blue dress, and a Green dress. The competition for prom queen is competitive,
and so each girl wants to stand out from the other girls. However, each girl also has
their own preferences with regards to the dress she likes the most. If a girl gets her
most preferred dress and is alone in wearing that dress, she gets a payoff of 3. If a
girl gets her second preferred dress and is alone in wearing it, she gets a payoff of 2.
Wearing her least preferred dress, but being the only one to do so earns her a payoff
of 1. If two girls are wearing the same dress, they both get their payoff of being alone
in the dress minus 1. If all 3 girls are wearing the same dress, they all get -3 to their
payoff.
Alejandra prefers Red to Blue and prefers Blue to Green. Brittany prefers Blue to Red
and Red to Green. Cho prefers Green to Red and Red to Blue. (Example: If A and B
are wearing Red and C is wearing blue, A will get a payoff of 3 - 1 = 2, B will get a
payoff of 2 - 1 = 1, and C will get a payoff of 1 - 0 = 1.) (20)
(a) (15) Write down the game in strategic form.
(b) (5) What are the pure strategy Nash Equilibria of the game? Underline the Best
Responses in the game above.

Added by Michael H.

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