The existing literature has made great achievements in technology sharing (licensing patents) contracts, which has defects in the selection of oligopoly models, the setting of innovation subjects, the consideration of product heterogeneity, and production costs. This paper aims to reveal the competitiveness strategies of leaders and followers for innovation, technology sharing, and sharing fees in a Stackelberg market. The three-stage sequential game method is used to achieve the objective. The results are as follows. First, whether an enterprise uses innovation or shares technology is related to the fixed cost of innovation, the return on innovation, and product differentiation. It will hinder innovation activities if the fixed cost of innovation is too high, the return on innovation is too low, or the products are too homogeneous. A relatively low return on innovation makes it possible for the two enterprises to engage in sharing. However, with a relatively high return on innovation, only a high level of product differentiation can ensure technology sharing. Second, the optimal sharing fee is dynamic, showing an upward and then downward trend as the return on innovation grows. Product differentiation has an uncertain impact on the cost. Third, either the leader or the follower is likely to be the optimal bearer of social responsibility depending on the returns on innovation and product differentiation. This study has theoretical significance for optimizing technology-sharing decisions, improving competitiveness for enterprises, and formulating effective industrial policy for the government. And it provides some practical guidance for competition and cooperation between enterprises with technological innovation behavior.