Game Theory · GT-28
Solve the last move first, then work backward — each earlier decision is made knowing exactly what the later ones will be.
A method for solving sequential games by starting at the final decision node, determining the optimal move there, then moving one step earlier and determining the optimal move given that known future response, repeating all the way back to the first move. It's the standard technique for finding subgame-perfect equilibria in games with a definite, known end.
The technique traces to Zermelo's 1913 analysis of chess and was formalized as a general solution method within the broader extensive-form game theory developed by von Neumann, Morgenstern, and later Reinhard Selten in the 1960s-70s.
The Mechanism
Solving a 3-move sequential game from the end backward
The solving order runs opposite to the playing order — you determine the last move first, because it requires no prediction, then use that certainty to solve each earlier move in turn. By the time you reach the actual first move, its optimal choice is fully determined by everything that follows.
01 · IT ELIMINATES NON-CREDIBLE THREATS AND PROMISES
The key refinement over plain Nash equilibrium
Backward induction is the method behind subgame-perfect equilibrium, which was developed by Reinhard Selten specifically to rule out Nash equilibria that rely on threats a player wouldn't actually want to carry out if the moment arrived — by solving from the end, you only ever accept moves that are genuinely optimal in every subgame, not just credible-sounding on paper.
02 · IT REQUIRES COMMON KNOWLEDGE OF RATIONALITY AT EVERY STEP
A demanding assumption that limits real-world predictive power
The method assumes every player is rational, expects every other player to be rational, expects them to expect that too, recursively — this chain of assumptions is exactly what the Centipede Game experiments (see Centipede Game) show breaking down in real human behavior well before the theoretical endpoint.
03 · IT ONLY APPLIES CLEANLY TO FINITE, PERFECT-INFORMATION GAMES
The scope condition
Backward induction requires a known, finite ending point and full visibility of prior moves — infinite or indefinitely repeated games (see Repeated Games & the Folk Theorem) and imperfect-information games require different solution techniques entirely, since there's no final node to start solving from.
Where It Fails / Inversion
Where it fails / inversion
Applying backward induction rigidly in settings with any uncertainty about whether the game will actually reach its theoretical final round, or where players might not be fully rational, systematically mispredicts real outcomes — the Centipede Game and finitely-repeated Prisoner's Dilemma experiments are the clearest illustrations of backward induction's logically sound but empirically unreliable predictions in practice.
How To Use It
Worked example · a phased negotiation with a known final deadline
A multi-round contract negotiation with a hard, known deadline (say, a fiscal year-end) can be usefully analyzed by working backward from that deadline: what will each side's best move be in the very last round, given no more rounds remain? That answer then informs what the optimal move is in the second-to-last round, and so on back to the opening offer. Skilled negotiators often do this instinctively — planning their opening position based on where they expect the endgame to land, not the other way around.
How to use it
When facing any multi-step decision with a known, finite endpoint, resist the urge to plan forward from where you are now — instead, work backward from the final decision point, solve that first, and let each earlier decision be shaped by what you now know the later ones will require. This consistently produces more coherent multi-step plans than forward-only reasoning.
See Also