Maximal guaranteed result in hierarchical games

A new method of investigation of hierarchical two-player games is discussed. This method consists of solving games with complex information exchanges using, for the most part, identical transformation of predicate calculus formulas. We introduce the notion of maximal guaranteed result in a game, give two definitions and discuss the relationship between them. The new method is illustrated on a classical example for which a maximal guaranteed result of a high level player in hierarchical game of two players is calculated. Some particular cases are discussed. Stability of this problem according to variation of the payoff function of the second player is analyzed. We also demonstrate how the definition, and, accordingly, the method are modfied for a benevolent or a bounded-rational second player. Also, we show that the new definiton is convenient for the investigation of stability of maximal guaranteed result calculation procedure with respect to the parameters of the game.