A generalization of the backward induction method in aligned games

We show that the well-known backward induction method generalizes to a broad class of sequential games and could be applied to find the entire set of perfect Bayesian equilibria and sequential equilibria. This is a class of games whose information sets appear in a clear chronological order. The computation of locally optimal strategies and the preconsistency check are performed stage-by-stage along the game tree. The full consistency check for computing sequential equilibria needs to be applied only to the perfect Bayesian equilibria at the end, thus reducing the computational work significantly. We fully characterize the class of games in which the generalized backward induction algorithm alone, without further full consistency check, yields the entire set of sequential equilibria.