Marta has three sons: Arturo, Bernardo, and Carlos. She discovers a broken lamp in her living room..

Marta has three sons: Arturo, Bernardo, and Carlos. She
discovers a broken lamp in her living room and knows that one of her sons must
have broken it at play. Carlos was actually the culprit, but Marta doesn’t know
this. She cares more about finding out the truth than she does about punishing
the child who broke the lamp, so Marta announces that her sons are to play the
following game. Each child will write down his name on a piece of paper and
write down either “Yes, I broke the lamp,” or “No, I didn’t break the lamp.” If
at least one child claims to have broken the lamp, she will give the normal
allowance of $2 to each child who claims to have broken the lamp, and $5 to
each child who claims not to have broken the lamp. If all three children claim
not to have broken the lamp, none of them receives any allowance (each receives
$0).

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(a) Write down the game table. Make Arturo the row
player, Bernardo the column player, and Carlos the page player.

(b) Find all the Nash equilibria of this game.

(c) There are multiple Nash equilibria of this game.
Which one would you consider to be a focal point?

 

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