On Ambiguities in the Interpretation of Game Trees

Piccione and Rubinstein have pointed out ambiguities in the interpretation of games of imperfect recall. They focus on the notion of time consistency, and argue that a player in a game of imperfect recall may be time inconsistent, changing his strategy despite no new information and no change in his preferences. In this paper it is argued that the apparent time inconsistency arises, in part, from an inappropriate definition of the notion. That is only part of the problem though. It is shown that in some cases the apparent time inconsistency, and, more generally, ambiguity in interpreting games of imperfect recall, stems from the fact that information sets in such games do not ingeneral capture all the relevant features of an agent's knowledge. A model is proposed, based on earlier work in the computer science literature, that does capture all these features.