This paper develops and presents some original game theory concepts utilizations for the formulation of companyâs cooperative and competitive strategies, having as basis the Strategic Games Matrix (SGM). The concepts and results from SGM are applied to analysis and formulation of entrepreneurial strategies, as a support tool to complex business structures strategic management - hierarchical or not - and for competitive and/or cooperative strategies, or a combinations of those. It is proposed a new typology for business strategic games derived from an analysis and interpretation of the SGM: Four classic strategic games types from game theory - Nash, Minimax, and Pareto, as nonhierarchical games, and Stackelberg, as a hierarchical game - are interpreted and applied to some conflict of interests situations; two new hierarchical strategic game types, applicable to limit-case situations, also derived from the SGM analysis - Dominant-Marginal, and Paternalist-Solidary - are also described and applied. A new methodology for analysis and design of competitive and cooperative strategy formulation for complex hierarchical structures strategic management, based on the SGM, is presented and applied to three level hierarchical games. The concepts of strategic scene-gaming, and of strategic dynamic positioning, are also introduced and illustrated.