If buyers are asymmetric in terms of their operating costs, researchers and managers broadly agree that the supplier can optimize her/his own profit by offering the more efficient buyer a higher price. In this paper, we develop a game theoretical model to investigate the interaction between one supplier and two asymmetric buyers within a supply chain. We formulate buyers' operating costs as a function of their process innovation levels, which implies that they can reduce the unit operating cost via investments in process innovation in the long run. Our research demonstrates that the uniform wholesale price (UWP) is always preferred over the buyer‐specific wholesale price by the supplier because of the effect of innovation stimulation. The optimal timing of pricing is contingent on the level of market demand variance. If two buyers have the same ability to reduce their operating costs via process innovation, the UWP strategy forms a win‐win situation to the supplier and two buyers. Our results provide the supplier with suggestions regarding when to adopt the UWP strategy and how to enhance downstream innovation performance within the supply chain.