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.

We study a simple motion differential game with many pursuers and one evader with equal capabilities in ${\mathbb{R}}^n$. The control functions of the players are subject to the Grönwall-type constraints. If the state of the evader coincides with the state of a pursuer, then the game is considered completed. If the state of the evader does not coincide with the state of any pursuer at all times, then we say that evasion is possible. We show that pursuit can be completed if a condition on the convex hull of the initial states of the pursuers is satisfied.