We develop a Culture Evolution Theory model to combine a bottom-up culture, in which innovation ideas are driven by bottom-up emergent social norms, with top-down incentives for innovation, where idea generators are given recognition by other employees. Culture influences innovation performance and productivity of the firm and is thus relevant for the organization's competitiveness. The model integrates three levels of competition and selection, at the level of employees, of the management of the company, and of competition among companies. This approach is able to illuminate how explicit strategy co-exists with implicit bottom-up driven cultural evolution of innovation.