 Both Moore (1992) and Pauly (2005) discuss the importance of reasoning about common knowledge and ignorance in the King Solomon cases. For example, King Solomon is ignorant of who is the real mother, but both women commonly know from the start who is the true mother, and that the true mother will therefore bid much higher than the other one. This makes the procedure safe. Again, epistemic logic and in particular common knowledge help to shed light on a tricky social procedure. For a more traditionally philosophical introduction to the fair division problem, including more extensive explanations of fairness, manipulability and envy-freeness, see the entry on  economics [normative] and economic justice.