Consider the bimatrix game ? = hI; J; A;Bi in complete and  1 inf  2  ? perfect information over the sets of pure strategies. So we can use the set of informational extended strategies I =  i = ? i 1 ; i 2 ; :::; i j ; :::i m
; = 1; nm      of the player 1 and J = n j =  j 1 ; j 2 ; :::; j i ; :::j n  ; = 1;mn o of the player 2 that mean the following: if the player 2 will choose the column j 2 J then the player 1 will choose the line i j 2 I and if the player 1 will choose the line i 2 I then the player 2 will choose the the column j i 2 J: The players do not know the informational extended strategies of each others. For these type of game it is very dicult to construct utility matrices: for all strategy pro le ? i ; j
which element of the matrix A and B should be considered as a payo value of the player 1 and 2 ? Thus, in order to solve games in informational extended strategies, we propose to use the following methodology. Using the informational extended strategies we construct the following normal form of the incomplete and imperfect information game e? = * f1; 2g; I; J;  AB( ; ) = a ij ; b ij j2J i2I  =1;mn =1;nm + : For the game e? we construct the associated Bayesian game ?Bayes = D f1; 2g;eI ;eJ ;A; B E ;where eI = S 2
1 eI( ) ; eJ = S 2
2 J( ): Here eI ( ) is the set of all pure strategy of the ?type player 1 and eJ ( ) the set of all pure strategy of ?type player 2: Payo matrices of the ?type player 1 and ?type player 2 are respectively A( )=  aei ej ej 2eJ( ) ei2eI( ) and B( )=  bei ej ej 2eJ( ) ei2eI( ) , where aei ej = P 2
2 p( = )a ij ; bei ej = P 2
1 q( j )b ij : The matrices A and B are the "big matrices", which consist of the submatrices type A( ) and B( ) respectively. It is true the following theorem Theorem. The strategy pro le  ei ;ej   is a Bayes-Nash equilibrium in the game ?Bayes if and only if it is a Nash equilibrium for the subgame sub?Bayes = D f1; 2g;eI ( );eJ ( );A( );B( ) E .