Many-to-many perfect matching

This paper considers a new type of two-sided matching in which multiple numbers of agents are perfectly matched on both sides. Such matching can be used between multiple major students and laboratories. The many-to-many perfect matching problem cannot be solved by existing many-to-many matching algorithms, since the perfect property, which is a global property, cannot be represented by the participants’ preferences, which are local properties. This paper gives a DA(Deferred Acceptance) mechanism to match each student to the given number of different laboratories without a blocking pair by introducing a master list of students to resolve ties between students.