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 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).

(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?