Prerequisites: Chapters 1 and 2.

All students in Soap College have to enroll either in FRE100 or ITA100 in their second semester. We assume that every student prefers one of them. There is a group of students, however, the “drama queens and kings”, who have strong likes and dislikes between their members, and for whom it is most important to be in a class with as many as possible of drama queens and kings they like and with as few as possible they dislike. A measure of this is the difference between the number of liked and the number of disliked drama queens or kings in the class. Only if this difference is the same for both classes would the drama queens or kings make their decisions according to their personal preferences for a language.

The dean at Soap College is concerned that many of the group members will end up in a class for social reasons, and assigns to us the task of investigating this problem.

The drama queens and kings don't care about other students in the course. They have strong feelings only about their fellow drama queens and kings. Group members could also be indifferent towards other group members. We can model this as a game by assuming that each group member gets a payoff of 9 for every group member he or she likes who is in the same class, and a payoff of -9 for every group member he or she dislikes who is in the same class, and an additional payoff of 1 if he or she gets the course for which he or she has a preference. The total payoff is the sum of the numbers.