Question

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 first woman whether the child is hers. If she

answers negatively, the child will be given to the second woman.

If she answers affirmatively, 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 first woman. If she

answers affirmatively, the second woman will pay the king 75

dinars, and receive the child, and first 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 first 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.

Answer 1

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