6. The Skill of Cybersecurity: Adversarial Thinking 135 Obviously, if they both accept the ruling and Solomon carries out his decision, the baby would die—neither woman would receive the baby in that case. If one woman rejects the ruling she is giving the baby to the other woman and risking the death penalty for herself. Even though the consequences for both women are symmetrical, what makes this game interesting is that they do not prefer the outcomes the same. This is because one of the two women is the living baby’s real mother. We can assume that the real mom loves her newborn baby and values her baby’s life above her own life—after all, she is fighting for her baby in court. This would not be true for the imposter who has already lost her baby and stolen this other baby. She values her own life above the life of the baby. Figure 6.4 shows what this game looks like in normal form, and it illustrates the asymmetry in the utility preferences. What combination of choices does the top-left square represent? (Mom: Accept, Imposter: Accept.) What is the outcome of this combination of choices? (Solomon carries out his ruling and the baby dies.) How do the women rank this outcome? (Even though she does not get to keep the baby, this is Imposter’s second best outcome because she loses nothing. It is Mom’s worst outcome because her baby dies.) Figure 6.4 Solomon’s wise ruling in normal form. Given these assumptions the game can be analyzed to identify the Nash equilibrium. To solve the game, start from Mom’s perspective and consider what she should do. In order for Mom to decide what she should do, she should first consider what Imposter might do and how she should respond. This is called best response analysis and is a helpful approach for solving games. If Imposter Rejects, what should Mom do? (Accept.) If Imposter Accepts, what should Mom do? (Reject.) Unlike in the prisoner’s dilemma, this approach has not clarified the situation—depending on Imposter’s choice, Mom should either Accept or Reject. However, Mom can go a level deeper. Putting herself in Imposter’s shoes, Mom can see what Imposter should do based on what Mom might do. If Mom Accepts, what should Imposter do? (Accept.) What if Mom Rejects? (Accept.) Now we are getting somewhere! No matter what Mom does, she can see that Imposter should Accept. This means that Reject is a dominated strategy for Imposter. A dominated strategy is a strategy that will never be chosen. With this insight, Mom can then determine what to do. Knowing that Imposter will choose Accept, what should Mom do? (Reject.)
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