Backward induction is a way to solve a sequential decision problem by reasoning from the end back to the beginning. In game theory, it is used to predict behavior in games with an order of moves and (typically) perfect information.
Core Mechanics (Rollback Logic)
The procedure is:
- Start at the final decision point (the last move) and choose the action that maximizes the decision-maker’s payoff at that point.
- Treat that choice as fixed, then move one step earlier and choose the best action given what will happen later.
- Continue until the first move.
In many settings, this yields a subgame perfect equilibrium: a strategy profile that is optimal in every subgame, not only along the path that is actually played.
Practical Example
Consider an entry game: an incumbent threatens a price war if a rival enters. If fighting entry is very costly to the incumbent, backward induction predicts that once entry happens, the incumbent will accommodate rather than fight. Knowing that, the rival enters. The initial threat is not credible because it would not be optimal when the time comes to carry it out.
Where It Can Mislead
Backward induction relies on strong assumptions (rationality and common knowledge of rationality). In some real settings, players may not reason fully backward, may care about reputation, or may make boundedly rational mistakes, so observed play can differ from the rollback prediction.