Backward Induction

Backward induction is the standard algorithm for finding 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 von Neumann and 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 effects, bounded rationality, or genuine uncertainty about other players' types, which is why subgame perfect equilibria sometimes make poor predictions in practice.