Game Theory and Solomon’s Wisdom
There is a very famous story about Solomon’s wisdom. N the story there are two new mothers, one of which who had smothered her baby during sleep and claimed the other woman’s baby as her own. The problem is presented to King Solomon, who proposes the baby be split in half, each woman receiving one half of the child. The woman who was lying agrees to the compromise, while the real mother immediately feels sympathy for her offspring. Rather than see her child killed, she says the baby belongs to the other woman. Solomon instantly gives the baby to the real mother, realizing that a true mother would compromise to see her offspring survive.
After learning game theory in class, let’s look at this story again. If both of the two women are experts in game theory, Solomon’s wisdom will fail. Assume woman A is the real mother and woman B is the liar. When Solomon asks to cut the baby into halves, A will definitely say no because she loves the baby and does not want to hurt it. On the other hand, if B understands game theory and think rationally, she will make the decision of giving the baby to A also. Now the situation is that both women A and B would like to give the baby to the other. We come back to the origin. Whether Solomon will cut the baby into halves or not, he cannot judge which woman is the baby’s real mother now. Solomon’s wisdom failed after learning game theory.
Is there any other method to solve the problem Solomon faces? Or is it still a puzzle?
1 comment:
There is an obviuous solution to this problem that we recently discovered in class: Coase theory.
Acting as a mediator in the dispute, Solomon could rule that either of the two women was the real mother. Using Coase theory, should he have chosen the wrong women the real mother will then attempt to buy the child back from the false mother (with probably everything she owns). If she isn't able to pay enough, then the child has wound up in the care of the person who 'valued' it most. A very cold way to look at the topic, yes, but economical.
On the other hand, should the child wind up in the hands of the true mother, it is very unlikely that the other woman will be able to offer the biological mother enough money to buy the child back.
Hmm... in this respect, I think the Coase theory actually fails? Due to the high transaction costs involved in the case of the real mother gaining the child, no private bargaining can occur... Although in this case the baby still winds up in the hands of who 'values' it most.
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