As e-commerce competition intensifies, brand companies face challenges such as product homogenization, consumer trust erosion, and price wars. Blockchain technology (BCT) has emerged as a solution to enhance transparency and optimize competitive strategies. In this study, the adoption of BCT and pricing decisions between weak and strong brand companies is analyzed in an asymmetric competitive environment. A game-theoretic framework is developed to analyze whether each company should adopt BCT. The results show that when the difference in brand awareness is small, BCT adoption allows pricing advantages to be shifted between weak and strong brands. As the difference in brand awareness increases, both types of brands reduce their BCT investments. Moreover, when one brand adopts BCT, the other often follows suit to maintain competitiveness. Three equilibrium scenarios are identified based on consumer privacy concerns and differences in brand awareness. Interestingly, the strategy where only the weak brand adopts BCT does not constitute an equilibrium in any scenario. Finally, when the difference in brand awareness is significant and price competition is high, either both brands adopt BCT or neither does. This paper provides strategic insights into BCT adoption and its implications for competitive behavior in asymmetric markets.