Three axioms from decision theory are applied to refinements of the Nash equilibria of a game in extensive form with perfect recall. One axiom requires that a refinement does not depend on embeddings within larger games that preserve the reduced normal form of the given game. Two further axioms require that a refinement selects subsets of equilibria that contain sequential equilibria, and that do not contain equilibria for which any player uses a strategy that is not an admissible reply. These axioms are satisfied by refinements that select subsets that are stable as defined by Mertens (1989). Conversely, for a game with two players, perfect information, and generic payoffs, the axioms are shown to imply that a selected set is the unique stable set.
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