The Solution of Scalar Bimatrix Games in Preferred Pure Strategies

In the present work the task of finding Nash equi-librium situation or finding the most preffered pure strategies in finite scalar m x n bimatrix Γ(A, B) game is studied. The problem of finding an equilibrium in the Γ(A, B) game has a long history, but due to the complexity of the known algorithms and methods, that cause various problems, its study is being continued today. Our approach is different from these methods. In order to find an equilibrium situation in the pure strategies, we mean making a prediction by each player about the second player's behavior for choosing preferred pure strategy. Therefore we use a sequential strictly and weakly procedure of dominance for comparing of two pure strategies. Only in the case of strictly dominance the line of dominance has no meaning in order to maintain an equilibrium situation in pure strategies. We don’t have such kind of situation in every game. In this kind of game each player can act by different principles to define the most preferred pure strategy, that is based on making a prediction about his partner’s behavior by the player and that means the orientation on guaranteed levels in concrete situations. We mean the orientation in A and B matrix games average V(A) and V( BT) playoffs obtained by the players using maximum optimal mixed strategies. Each player’s decisions are discussed about the usage the preferred pure strategies related to his partner’s actions. By using them he will gain much more, then in an equilibrium situation. All kinds of other actions are also discussed. Acceptable results are used for solution of high ranged m x n (m>2, n>2) Bimatrix Γ(A, B) games.