The logic of backward induction

The logic of backward induction (BI) in perfect information (PI) games has been intensely scrutinized for the past quarter century. A major development came in 2002, when P. Battigalli and M. Sinischalchi (BS) showed that an outcome of a PI game is consistent with common strong belief of utility maximization if and only if it is the BI outcome. Both BS’s formulation, and their proof, are complex and deep. We show that the result continues to hold when utility maximization is replaced by a rationality condition that is even more compelling; more important, the formulation and proof become far more transparent, accessible, and self-contained.