About One Model Strategic Game of Collective Choice

A model of dyadic non-cooperative game ) (H Γ is discussed in the paper for the set of one and the same players' strategies.The players make their choice sitting round the table and have the opportunity to coordinate only the meanings of utilities in every situation.Therefore the players' payoffs are given by 2 2 × matrixes.A notion "the equalized situation" in mixed strategies which is at the same time the equilibrium is introduced.The theorem has been proved, which establishes the conditions of existance of an equalized situation in the given game.In the case of the existence algorithm is constructed.If equalized situation doesn't exist in the game, then there exists the equilibrium situation in the pure strategies and it is possible to find it by analysis of situations. ) (H Γ game's with bimatrix Γ game in case of two players is given.The players' conditions of optimal mixed strategies existence in Γ game is written.Relevant examples are solved and ) (H Γ game's application for finite amount of players' is discussed.