This study presents a vertical supply chain model that considers bargaining power to explore independent innovation and co‐innovation decisions and their impacts and analyzes the optimal subsidy strategy for co‐innovation. We find that collaboration promotes technology innovation. Increases in consumer innovation preferences and government subsidies are conducive to co‐innovation. Both independent and co‐innovation can promote Pareto improvements under limiting conditions. Government subsidies can improve co‐innovation performance, but the subsidy parameter needs to be regulated. The optimal subsidy strategy is influenced by the subsidy target and budget. Governments prefer an innovative degree subsidy or a production cost subsidy.