7. Two children have two lollipops each. Each child can observe his or her own strength but not the other child's strength, where each child's strength is uniformly distributed between 0 and 1. The two children simultaneously decide whether or not to quarrel. If at least one child decides to quarrel, then the stronger child gets all four lollipops and the weaker child gets none. If neither child wants to quarrel, they each end up with two lollipops. a. Formulate this situation as a Bayesian game. b. Find all Nash equilibria of this game. c. How would your answer to (b) change if one of the lollipops is destroyed when the children quarrel, such that the stronger child only gets three? d. How would your answer to (b) change if child A decides rst whether to quarrel or not, then child B, observing A's choice, chooses whether to quarrel or not? (Again, a quarrel happens if and only if at least one child chooses to quarrel.)