Uncertain information structures and backward induction

Abstract

In everyday economic interactions, it is not clear whether sequential choices are visible or not to other participants: agents might be deluded about opponents' capacity to acquire, interpret or keep track of data, or might simply unexpectedly forget what they previously observed (but not chose). Following this idea, this paper drops the assumption that the information structure of extensive-form games is commonly known; that is, it introduces uncertainty into players' capacity to observe each others' past choices. Using this approach, our main result provides the following epistemic characterisation: if players (i) are rational, (ii) have strong belief in both opponents' rationality and opponents' capacity to observe others' choices, and (iii) have common belief in both opponents' future rationality and opponents' future capacity to observe others' choices, then the backward induction outcome obtains. Consequently, we do not require perfect information, and players observing each others' choices is often irrelevant from a strategic point of view. The analysis extends -from generic games with perfect information to games with not necessarily perfect informationthe work by Battigalli and Siniscalchi (2002) and Perea (2014), who provide different sufficient epistemic conditions for the backward induction outcome.