View source for Backward Induction

'''Backward induction''' is the standard algorithm for finding [[Subgame Perfection|subgame perfect equilibria]] in sequential games. The method solves the game from the final decision nodes backward to the initial node: at each step, a player chooses the action that maximizes their payoff, given the known optimal choices at all subsequent nodes. The result is a strategy profile that is rational at every point in the game tree, not just in equilibrium.

The technique was implicit in [[John von Neumann|von Neumann]] and [[Oskar Morgenstern|Morgenstern]]'s foundational work, but it was [[Reinhard Selten]] who formalized its connection to subgame perfection. Backward induction is not merely a computational convenience — it encodes a substantive assumption about rationality: that players' future choices are predictable from their incentives, and that this predictability is itself known to all players. This assumption fails in games with [[Reputation (game theory)|reputation effects]], [[Bounded Rationality|bounded rationality]], or genuine uncertainty about other players' types, which is why subgame perfect equilibria sometimes make poor predictions in practice.

[[Category:Mathematics]]
[[Category:Systems]]