Summary: Hierarchical decomposition is applied to the payoff matrix of a 2-player zero-sum noncooperative game. Relationship between the strategy vector of the integrated payoff matrix and the strategy vector of each decomposed payoff matrix is studied. For the case of 2×2 zero-sum noncooperative game with purely mixed strategies, a simple formula which relates the strategy vector of the integrated payoff matrix and the strategy vector of each decomposed payoff matrix is established; the strategy vector of the integrated payoff matrix is obtained as a weighted combination of the strategy vector of each decomposed payoff matrix with the weight considering both the priority weight of each decomposed payoff matrix (or payoff matrix for each criterion) and
the magnitude of each decomposed payoff matrix. The higher layer integrated game corresponds to the strategic decision making and the lower layer decomposed games correspond to the tactical decision making.Keywords: zero-sum game, payoff matrix, decomposition, strategy, tactics
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