Exchange-proofness or divorce-proofness? Stability in one-sided matching markets

Two stability concepts for one-sided matching markets are analyzed: Gale-Shapley stability and ξ-stability. The first one applies best to markets where no status quo allocation is considered, whereas the second one is a solution to be used when property rights are allowed. A common problem of existence is shared by both solution concepts. Hence, we study economic environments where this problem does not exist, and present a family of agents’ preferences for which existence is guaranteed for both Gale-Shapley stable and ξ-stable outcomes. This work was finished while the author was visiting Duke University, whose hospitality is gratefully acknowledged. Swveral discussions with Salvador Barberà, Hervé Moulin and Marilda Sotomayor and some advice by an anonymous referee were specially useful. This work is partially supported by Grants PB 92-0590 and PB 93-0938 from the DGICYT, the Spanish Ministery of Educación Ciencia, and the Institut Valencià d’Investigacions Econòmiques.