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Unique Stability in Simple Coalition Formation Games

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Working paper
Szilvia Papai
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 proļ¬le when only admissible coalitions may form. An alternative characterization of unique stability is also provided, based on a graph- theoretic 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.
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