An equilibrium strategy for each student to enter a certain department in a university

In a certain university, first year students do not belong to any department. But starting with their second year they must enter some department. In each department there are quotas as to the number of students who may enter the department, and in determining which students can enter which department two kinds of data are considered, namely 1: the student’s class rank and 2: the student’s declared preference which shall be called ‘Delcaration of Preferences’. If it is assumed that the rank and true preferences of each student is known by all other students, then according to their ranks and preferences, each student should be able to produce a strategy for making their declaration. In this case, there exists an equilibrium strategy. The authors show the existence of an equilibrium strategy through an algorithm that maps each student’s preference to an optimal declaration strategy. In addition, using a program that determines an equilibrium strategy they perform a simulation to determine the relationship between each student’s class rank and the expected rank, in terms of his or her true preferences, of the department which the student will eventually enter. [In Japanese.]