The game mechanism on R&D innovation strategy of groups of firms has been researched by method of management mechanism design in the paper. First, the firms' competitive advantage, core competence, core specialties, strategic fit, strategic flexibility, and critical strategic factors affecting firms' performance and competition are explored and summed up. Second, as aspect of decision making mechanism a model that describes the processes of strategic competition for groups of firms is built on the basis of management mechanism analysis. Thus, the processes of evolution for group of firms to innovate in R&D each other are shown in the model and some conclusions can be deduced under the conditions and constraints, such as different business environments and contexts. Finally, through the processes of evolution for firms to compete in R&D innovation, some policy suggestions and measures that Coordinate and control firms' strategic behavior are presented. The policy suggestions and measures are about what like environments and contexts that the firms to compete fairly in should be created by government, how to trade off between monopoly and super-competition etc.