In response to the demand for carbon emission reduction, enterprises engage in green technology innovation. Technical collaboration between rival companies has emerged as a strategy to lower the costs of green innovation, reduce uncertainties and risks, and meet market demands by accelerating the introduction of new products. This paper establishes three game models based on the different cooperation contracts of the heterogeneous brand firms: the non‐cooperative model, the innovation cost‐sharing contract model, and the technology licensing contract model. Comprehensive analysis shows that competing firms intend to cooperate based on reducing green innovation costs and producing products with higher green levels to meet the market. Although cooperation between competing firms is beneficial for the profit gaining of both firms, the cooperation does not necessarily lead to an increase in the green level of products. Comparing with the cost‐sharing contract, although technology licensing may highlight the brand disadvantage of the emerging enterprise under significant disparity in brand differentiation, the emerging enterprise can still benefit from increased sales generated by the dominant enterprise and achieve higher gains. Furthermore, competing firms can achieve a win‐win‐win situation in terms of profit, environment, and social welfare through both cost‐sharing contract and technology licensing contract under certain circumstances.