Rethinking common belief, revision, and backward induction

• I consider backward induction in finite, extensive form, perfect information games.
• I argue that the structure of common beliefs warrants a constraint on their revision.
• I augment the AGM theory of belief revision with this constraint, yielding “AGM+”.
• AGM+ prevents un-forced revision from common belief in rationality to irrationality.
• Rationality and common belief in rationality entail backward induction.

Whether rationality and common belief in rationality jointly entail the backward inductive outcome in centipede games has long been debated. Stalnaker’s compelling negative argument appeals to the AGM belief revision postulates to argue that off-path moves may be rational, given the revisions they may prompt. I counter that the structure of common belief and the principles of AGM justify an additional assumption about revision. I then prove that, given my proposed constraint, for all finite, n-player, extensive form, perfect information games with a unique backward inductive solution, if there is initial common belief in rationality, then backward induction is guaranteed.