Sequentially stable outcomes

This paper introduces and analyzes sequentially stable outcomes in extensive games. An outcome ω is sequentially stable if for any ε >0, any version of the game where players make mistakes with small enough probability has a perfect ε-equilibrium with outcome close to ω. Unlike stable outcomes (Kohlberg and Mertens, 1986), sequentially stable outcomes exist for all finite games and are sequentially rational. If there is a unique sequentially stable outcome, such an outcome is the unique stable outcome of the game’s agent normal form. Also, sequentially sta-ble outcomes satisfy versions of forward induction, iterated strict equilibrium dominance, and invariance to simultaneous moves. In signaling games, sequentially stable outcomes pass the standard selection criteria, and when payoffs are generic, they coincide with stable outcomes.