I cannot find any difference, except for that the subgame perfect Nash-equilibrium yields a strategy rather than an action, between those two solution concepts. To me, it seems like you always just use backwards induction when finding the subgame perfect Nash-equilibrium. If that is the case, why would you spend time defining two things that really are the same (if I am not being wrong, which I guess I am)?
2026-05-14 12:18:14.1778761094
What is the difference between subgame perfect Nash-equilibrium and backwards induction?
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They are not really the same thing. Sub-game perfectness of a solution like the Nash equilibrium is a desirable consistency property of a solution concept, i.e., no sub-group of players should have an incentive to deviate from a Nash-equilibrium to play from a particular node onward their own sub-game to improve their payoffs.
However, backwards induction is a solution procedure to compute Nash-equilibria of a game while making use of the desirable feature of sub-game perfectness of that solution concept.