Perfect aggregation of information in two-person multistage games with fixed sequence of moves and aggregated information on partner's choice

Two-person multistage game with fixed sequence of moves is considered, under perfect information on existing history of the game and aggregated information on the current move of player 2. Having this information at each stage i, player 1 is the first to choose his move x(in1)(.); moreover, in the beginning of the game player 1 announces his strategy x(.)=(a(in1)(.),…, x(in)(.)) for n future stages. Given information regarding the choice of player 1 and history of the game, player 2 strives to maximize his payoff function via the strategy v=(v(in1), v(in2),…, v(inn)). In this paper the sufficient conditions of perfect aggregation, involving certain results from the theory of Lie groups, are provided for the game in question.