On a repeated game without a recursive structure

The solution is given here for the infinitely repeated two-person zero-sum games of incomplete information characterized by 2×2 games, with information matrices$left( {{*{20}c} a & b b & b } right)$left( {begin{array}{*{20}c} a & b b & b end{array} } right) for the first game and$left( {{*{20}c} b & b b & a } right)$left( {begin{array}{*{20}c} b & b b & a end{array} } right) for the second game.