SubgamePerfect

Subgame perfect equilibrium is a refinement of Nash equilibrium used in game theory. It addresses games that can be broken down into smaller sequential subgames. A strategy profile is considered a subgame perfect equilibrium if it constitutes a Nash equilibrium in every subgame of the original game. This means that at any point in the game, a player's strategy must be optimal for them, given the strategies of the other players, not only from the beginning of the game but also from any subsequent decision point.

The concept is particularly important for analyzing sequential games, where players make decisions over time and have information about previous moves. Backward induction is a common method used to find subgame perfect equilibria. This involves starting from the end of the game and working backward, determining the optimal strategy at each decision node, assuming that future players will also play optimally.

A strategy profile that is a subgame perfect equilibrium is always a Nash equilibrium. However, the converse is not necessarily true; a Nash equilibrium may not be subgame perfect. This is because a Nash equilibrium might prescribe actions that are not optimal in a subgame that is never reached under the equilibrium path. Subgame perfection eliminates non-credible threats, ensuring that strategies remain optimal even in hypothetical future scenarios.