Stable matching and protocol-free equilibrium

Abstract We consider a non-cooperative decentralized matching game as sequential bargaining. A protocol-free equilibrium is a subgame perfect equilibrium which is robust to a choice of a bargaining protocol. We show that a matching is generated in a protocol-free equilibrium if and only if it is stable. The bargaining game can be applied to a wide class of matching problems including marriage problems, college admissions problems, matching with contracts, assignment games, and cooperative NTU games.