Econ: Seminar in Microeconomic Analysis

Game theory questions required detail answer and process.

1. (20 points) Two women appear before King Solomon at his palace, along with an infant. Each woman claims that the infant is her child. The child is “worth” 100 dinars to his true mother, but he is only “worth” 50 dinars to the impostor. The king knows that one of the two women is the true mother of the child, and he knows the “values” that the true mother and the impostor ascribe to the child, but he does not know which woman is the true mother, and which the impostor. To determine which of the two women is the true mother, the king explains to both women that he will implement the following steps:

(a) He will ask the fifirst woman whether the child is hers. If she answers negatively, the child will be given to the second woman. If she answers affifirmatively, the king will continue to the next step.

(b) He will ask the second woman if the child is hers. If she answers negatively, the child will be given to the fifirst woman. If she answers affifirmatively, the second woman will pay the king 75 dinars, and receive the child, and fifirst woman will pay the king 10 dinars.

i. Assume that each woman has a payoff of 0 dinar if she does not receive the child. Draw the game tree when (a) The fifirst woman is the true mother and when (b) The second woman is the true mother.

ii. Find and report the subgame perfect equilibrium under (a) and (b), and describe what happens (who gets the child and how much is paid by each woman) in each equilibrium.