Subgame perfect equilibrium

A strategy profile in an extensive-form game is subgame perfect if it forms a Nash equilibrium in every subgame, including the whole game. This rules out plans that rely on noncredible threats.

Backward induction: A method for solving sequential games by reasoning from final decisions toward earlier ones. In finite games with perfect information, it constructs subgame perfect equilibria by solving each decision point in turn.
Entry deterrence: A strategic setting in which an incumbent tries to discourage a potential rival from entering a market. A promise to wage a costly price war after entry may fail the subgame perfection test.
Perfect Bayesian equilibrium: An equilibrium concept for extensive-form games that combines sequential rationality with consistent beliefs. It handles beliefs at information sets, including cases where ordinary subgames are unavailable.
Game tree: A branching diagram representing the sequence of decisions and outcomes in a game. Its decision nodes and branches make candidate subgames visible.
Reinhard Selten: A German economist who developed key refinements of Nash equilibrium and shared the 1994 Nobel Memorial Prize in Economic Sciences. Selten introduced subgame perfection to formalize credibility in dynamic games.
Extensive-form game: A game represented by decision nodes, actions, information sets, and outcomes. Subgames and complete strategies are defined using this representation.
Stackelberg competition: A quantity-setting market model in which one firm chooses output before its rival. Backward induction selects the follower's best response and then the leader's optimal output.
Sequential equilibrium: An equilibrium concept requiring strategies to be sequentially rational given consistent beliefs at every information set. It refines equilibrium in games with imperfect information more directly than subgame perfection alone.
Information set: A set of decision nodes a player cannot distinguish when choosing an action. A subgame cannot begin at a node that splits an information set.
Nash equilibrium refinement: A stricter equilibrium concept that eliminates some Nash equilibria using additional rationality or robustness requirements. Subgame perfection became one of the foundational refinements for strategic games.

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