A child chooses whether to sneak a cookie from the cookie jar (C) or not (N ). Simultaneously, the child's parent chooses whether to punish the child (P ) or not. The child gets utility 2 from a cookie, and utility −3 from being punished; the parent gets utility −1 from their child sneaking a cookie, and utility −1 from punishing the child. Thus, if the child is the row player and the parent is the column player, the game's payoffs are N P N 0, 0 −3, −1 C 2, −1 −1, −2 1.a Suppose the parent observes the child sneaking a cookie (that is, moves are not simultaneous). Should they punish the child, or not? What if they observe the child not taking a cookie? 1.b In the Nash equilibrium of this game, does the child take a cookie or not? Now, suppose that the child and the parent both discount the future at rate δ. 1.c Does your answer to part (b) change if the game is repeated a finite number of times? 1.d Does your answer to part (b) change if the game is repeated an infinite number of times?

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Lets analyze each part of the question 1a If the parent observes the child sneaking a cookie they face the choice of punishing or not punishing the ch... View the full answer