We consider two competing firms in a competitive industry, modeled as proposed by J. P. Gould. Assuming that one company is a start-up and the other company is a well-established one with a dynamic behavior determining the optimum, we take the point of view of the start-up. We propose a pinning control scheme that makes the solutions of the start-up in capital stock and gross investment rate approach the solutions of the company determining the desired behavior. The approach is discussed based on numerical examples. An extension of the proposed control law equips it with the capability to cope with uncertainties. We interpret our findings from the perspectives of control theory and economics.
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