Subgame Credible Nash Equilibrium

We propose the Subgame Credible Nash Equilibrium (SCNE), a refinement of subgame perfect Nash equilibrium (SPNE) for multi-stage games. SCNE retains the internal credibility requirement of SPNE -- equilibrium behavior in every subgame -- and adds an external credibility requirement across equivalent subgames: whenever a player's prescribed continuation strategy differs across equivalent subgames, her own continuation payoff must not decrease. The intuition is that credible punishments or promises should not strictly harm the punisher relative to an equivalent no-punishment subgame. The SCNE eliminates equilibria sustained by self-harming punishments or promises while preserving existence. Every multi-stage game admits an SCNE, and if each stage game has a unique Nash equilibrium, the SCNE is unique.