Unique stability in simple coalition formation games

We investigate the uniqueness of stable coalition structures, when the value of a coalition to a member depends solely on the identity of the other members of the coalition. We give a complete characterization of collections of coalitions which ensure that there is a unique stable coalition structure at every preference profile when only admissible coalitions may form. An alternative characterization of unique stability is also provided, based on a graphtheoretic representation of collections of coalitions. We explore the implications of our characterization results for matching problems and the existence of strategyproof rules of coalition formation. Journal of Economic Literature Classification Numbers: C71, C78, D71. Proposed running head: COALITION FORMATION GAMES Corresponding author: Szilvia Pápai Department of Finance and Business Economics Mendoza College of Business University of Notre Dame Notre Dame, IN 46556, USA