Sequences in Pairing Problems: A New Approach to Reconcile Stability with Strategy-Proofness for Elementary Matching Problems
We study two-sided ("marriage") and general pairing ("roommate") problems. We introduce "sequences," lists of matchings that are repeated in order. Stable sequences are natural extensions of stable matchings; case in point, we show that a sequence of stable matchings is stable. In addition, stable sequences can provide solutions to problems for which stable matchings do not exist. In a sense, they