On the representation of informational structures in games

We consider two well-known mathematical representations of informational structures in game theory. The first is based on the set of historical sequences of information encountered in the game while the second is given by the informational digraph of the game. We show that while the latter can always be embedded into the former under some mild technical condition, the converse does not hold in general. We give a necessary and sufficient condition for an informational digraph to be equivalent to a sequence theoretic informational structure and discuss the relevance of this result to game theory.