Dynamic game results of the acquisition of new technology

Open- and closed-loop Nash strategies are derived and analyzed for a differential game in which two competing firms choose prices and productive capacity where new technology reduces a firm’s unit operating cost. Using an open-loop strategy, a firm makes an irreversible commitment to a future course of action. For example, a contract with a labor union may force a firm to commit to maintaining its entire workforce regardless of its competitor’s future realized behavior. In contrast, using a closed-loop strategy, a firm’s decisions evolve over time, continuously responding to the competitor’s behavior. The dynamic Nash strategies obtained for the closed-loop model exhibit a more restricted acquisition of new technology and a greater reduction of existing capacity relative to the open-loop solutions. In addition, the dynamic Nash price to be charged for output is higher in the closed as opposed to open-loop competitive environment. Numerical solutions are presented to demonstrate that if both firms apply the closed-loop approach, each will earn higher profits than if one or both firms choose an open-loop strategy.