Three friends (Julie, Kristin, and Larissa) independently go shopping for dresses for their…

Three friends (Julie, Kristin, and Larissa) independently
go shopping for dresses for their high-school prom. On reaching the store, each
girl sees only three dresses worth considering: one black, one lavender, and
one yellow. Each girl furthermore can tell that her two friends would consider
the same set of three dresses, because all three have somewhat similar tastes.
Each girl would prefer to have a unique dress, so a girl’s utility is 0 if she
ends up purchasing the same dress as at least one of her friends. All three
know that Julie strongly prefers black to both lavender and yellow, so she
would get a utility of 3 if she were the only one wearing the black dress, and
a utility of 1 if she were either the only one wearing the lavender dress or
the only one wearing the yellow dress. Similarly, all know that Kristin prefers
lavender and secondarily prefers yellow, so her utility would be 3 for uniquely
wearing lavender, 2 for uniquely wearing yellow, and 1 for uniquely wearing
black. Finally, all know that Larissa prefers yellow and secondarily prefers
black, so she would get 3 for uniquely wearing yellow, 2 for uniquely wearing
black, and 1 for uniquely wearing lavender.

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(a) Provide the game table for this three-player game.
Make Julie the row player, Kristin the column player, and Larissa the page
player.

(b) Identify any dominated strategies in this game, or
explain why there are none.

(c) What are the pure-strategy Nash equilibria in this
game?

 

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