The dilemma of Solomon ... revised with Game Theory

In the Bible - in the "First Book of Kings" it is told the story of King Solomon and his legendary ability to judge. One incident in particular the life of the mythical king made history: the story of the two women and the child contended.

Then two prostitutes came to the king and stood before him. One of the women said, "O my lord, this woman and I live in the same house; I gave birth when she was at home. Three days after I gave birth, this woman also gave birth; and there was no else in the house except the two of us. The son of this woman died at night, because she lay on him for you. She then stood up in the middle of the night, took my son from my side, while your maidservant slept, and laid it in her bosom, and my breasts laid her dead son. When in the morning I got up to nurse my son, I found that he had died; But when I examined him carefully in the morning, I saw it was not the son I had borne. " Then the other woman said, "It is not true; my son is alive, and yours is the dead one. " But first he insisted: "It is not true; your son is dead, and my living one. "

[...] Then the king commanded, "Bring me a sword." So they brought a sword before the king. The king then ordered, "Divide the living child in two and give half to one and half to the other." Then the child alive woman, whom he dearly loved his son, said to the king, "Please! My lord, give her the living child, but do not kill him! "But the other said," It shall be neither mine nor thine, but divide it. " The king answered and said, "Give her the living child, and do not kill him, because she is the mother of the child."

Duplicity. The second woman, calmly accepting the Solomon decision proved, his duplicity. However, it was very naive, because it was obvious that his behavior would unmasked. In fact he should imitate the real mother and show distraught as she was. At that point, Solomon would have to show consistent cutting in two the child, or reveal his bluff without having resolved the dilemma.

What it would have done instead? Here is a possible answer suggested by game theory, inspired by the book The Art of Avinash K. Dixit and Barry J. Nalebuff Strategy (Tea). Knowing that the two women, let's call Anna and Bathsheba, had very similar financial resources (the Bible, in fact, suggests that both were prostitutes who worked in the same "house"), Solomon could have issued the following judgment:

"Anna will speak first (1) and will have the last chance to give up the child without having to pay a fine for having bothered; if you insist in its request, the word will go to Bathsheba;

in turn, Bathsheba (2) will have the opportunity to give up the child without pay the fine or to establish for it a price to pay me;

the last to speak (3) will be Anna, who will give up the child by paying the fine or exceed the price offered by Bathsheba; if it does, Bathsheba will have to give to the child and also to pay the fine. "

SOLUTION IMMORAL. This solution is much more complicated than that of the Bible, and also seems a bit 'immoral because it brings up fines and price tags. In reality, however, no one will pay anything because the false mother immediately renounce his claims in front of the risk of being left without a son and without money. That's why.

(1) Suppose that the liar is Anna: knowing that Bathsheba, when it is his turn, will give everything he has, it will not be willing to ruin for the child of another and then give up now and do not have to do this after paying well fine.

(2) Suppose that the liar is Bathsheba: Anna insists in his request and if she comes, will his turn, will establish a price for the child, it is virtually certain that Anna will exceed forcing her to pay the fine losing the baby. You'd better give up a lot more.