Based on Experiment 5. Demonstrates how a third-party can harness strategic thinking to make inferences about player identities or motivations; based on Brams. 2003. Biblical games: game theory and the Hebrew Bible.
In Chapter 3 of the First Book of Kings, two women stand before King Solomon. Both claim to be the mother of a baby boy (one is the mother and one is the mother of a dead baby; both women live in the same house). King Solomon proposes a solution: "Cut the live child in two, and give half to one and half to the other (1 Kgs. 3:25)." Why is King Solomon widely regarded as a wise man, rather than an insane despot? Because he thought about the incentives the two women faced and structured a game that reveals the women's identities through their actions.
The King assumes that the women care both about the baby and winning Solomon's favor, but the real mother cares more about the baby and the imposter cares more about winning Solomon's favor. Both women can either oppose the King's solution or not oppose it. If both oppose the solution, the baby is surely saved. If the mother opposes the solution and the imposter does not oppose the solution, the baby may potentially be saved and given to the mother, but it may also be killed. The imposter, however, believes she will win the favor of the King. If the mother does not oppose the solution and the imposter does oppose the solution, the baby may potentially be saved and, if so, will go to the imposter. If neither the mother nor the imposter protests the solution, the baby will surely be killed.
The following game matrix, which you saw in Experiment 5, captures the essence of the situation. Payoff values are: 4= best; 3= next best, 2= next worst, 1 = worst.
The mother has a dominant strategy to Oppose the Solution and the imposter has a dominant strategy to Not Oppose the Solution. Thus their choice of strategies will likely reveal their identities.
Sure enough, "[T]he woman whose son was the live one pleaded with the king, for she was overcome with compassion for her son. 'Please, my lord,' she cried, 'give her the live child; only don't kill it!' The other insisted, 'It shall be neither yours nor mine; cut it in two!' " (1 Kgs. 3:26).
Of course, you might wonder to yourself, why didn't the imposter realize what the King was doing and change her strategy accordingly. That question would require more game theory and perhaps some concepts from behavioral economics. Take more economics courses and you might be able to answer it!