To win a sequence of moves, reason from the LAST one backward: at each step, ask what the other will actually do when it’s their turn — not what they THREATEN. A threat that would hurt the threatener to carry out is not credible, and a sharp rival will call the bluff. That’s why deterrence needs commitment, not bluster. Slide to walk the tree from its leaves.
Backward induction solves a sequential game from its final decisions upward, keeping only choices that are optimal WHEN REACHED — yielding the subgame-perfect equilibrium and pruning non-credible threats. Entry deterrence: an incumbent threatens a price war if a rival enters, but fighting pays the incumbent 0 while accommodating pays 2 — so at that node it will ACCOMMODATE. Foreseeing this, the entrant enters. The threat is empty; only a binding COMMITMENT (that makes fighting actually optimal) would deter. A fail-loud self-check throws unless backward induction discards the fight threat and predicts entry. ◆ real game theory, node-verified.
A two-stage entry game (the exact subgame-perfect logic); real deterrence adds reputation across many rivals and incomplete information that can make fighting rational — the prune-non-credible-threats mechanism is exact.