Subgame Perfection

A subgame perfect equilibrium is a refinement of the Nash equilibrium concept that eliminates strategies relying on non-credible threats. In extensive-form games — games played over time with sequential moves — a Nash equilibrium may include threats that a rational player would never actually carry out if called upon. Subgame perfection requires that players' strategies constitute Nash equilibria in every subgame, not just the game as a whole.

The concept was introduced by Reinhard Selten in 1965 and is now the standard solution concept for dynamic games. It captures the intuition that rationality should be consistent across time: a strategy that is optimal at the beginning of the game should remain optimal at every decision point, given the information available. The standard method for finding subgame perfect equilibria is backward induction, which solves the game from the final moves backward to the first.