Subgame Perfect Equilibrium
A Nash equilibrium that also prescribes a Nash equilibrium in every subgame.
Definition
A strategy profile is a subgame perfect equilibrium if its restriction to every subgame is a Nash equilibrium of that subgame.
Found via backward induction in finite games of perfect information.
Intuition
Rules out non-credible threats by requiring rational play even off the equilibrium path.
A refinement of Nash that respects sequential rationality.
Worked example
In Stackelberg competition, the SPE is the leader-follower outcome obtained by backward induction.
In the entry-deterrence game, threats to fight that would be irrational ex post are not subgame perfect.
The math
Selten (1965) introduced SPE; for finite perfect-information games it coincides with the backward-induction path.
Zermelo's theorem guarantees existence in finite perfect-information games.
Where it is used
Sequential bargaining, dynamic oligopoly, and repeated-game analysis.
Essential when credibility of continuation play matters.
More in Game theory
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