Backward Induction

Abstract

In recent years, two influential contributions on backward induction infinite perfect information games have appeared, namely Aumann (1995) and Ben-Porath (1997). These contributions—both of which consider generic perfect information games (where all payoffs are different)— reach opposite conclusions: While Aumann establishes that ‘common knowledge of rationality’ implies that the backward induction outcome is reached, Ben-Porath shows that the backward induction outcome is not the only outcome that is consistent with ‘common certainty of rationality’. The models of Aumann and Ben-Porath are different. One such difference is that Aumann makes use of ‘knowledge’ in the sense of ‘true knowledge’, while Ben-Porath’s analysis is based on ‘certainty’ in the sense of ‘belief with probability one’. Another is that the term ‘rationality’ is used in different senses: Aumann imposes rationality in all subgames, while Ben-Porath assumes rationality initially, in the whole game, only (not after a “surprise” has occurred).