Consider a game between a parent and a child. The child can choose to be good...

Consider a game between a parent and a child. The child can choose to be good (G) or bad (B); the parent can punish the child (P) or not (N). The child get enjoyment worth a 1 from bad behavior, but hurt worth -2 from punishment. Thus, a child who behaves badly and is punished gets 1 - 2 = -1; and so on. The parents gets -2 from the child's bad behavior and -1 from inflicting punishment.

(a) Set up this game as a simultaneous-move game, and find the equilibrium

(b) Next, suppose that the child chooses G or B first and that the parent chooses its P or N after having observed the child's action. Draw the game tree and find the subgame-perfect equilibirum.

(c) Now suppose that before the child acts, the parent can commit to a strategy. For example, the threat "P if B" ("If you behave badly, I will punish you"). How many such strategies does the parent have? Write the table for this game. Find all pure-strategy Nash equilibria.

(d) How do your answers to part (b) and (c) differ? Explain the reason for the difference.

Expert Solution

Rahul Sunny answered 2 years ago

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