Many-step two-person games with a fixed sequence of moves under aggregated information on partner's choice

A many-step two-person game is studied with a fixed sequence of moves under aggregated information on every move at the decision making instant and on the choice of player 2 at the current move. Player 1, knowing this information at every step $i$, first chooses a strategy $\mathbf{x}_{i}(\cdot)=({\mathbf{x}}_{1}(\cdot),\dots,{\mathbf{x}}_{n}(\cdot))$, $i=\overline{1,n}$, and informs it for $n$ moves to player 2 at the beginning of the game. His maximal guaranteed result and the corresponding optimal ($\varepsilon$-optimal) strategy are determined. Such games under complete (nonaggregated) information are formulated and a compact expression for the strategy of player 1 is derived.