A Game-Theoretic System Model for BOPS Integration Under Heterogeneous Online Reviews

Retailers increasingly adopt “Buy Online, Pick Up in-store” (BOPS) to coordinate online and offline channels, yet the role of heterogeneous online reviews in shaping BOPS adoption and pricing remains insufficiently understood. This study develops a duopoly game-theoretic model in which two retailers, facing asymmetric review quality, decide whether to integrate channels through BOPS or operate them separately. We characterize equilibrium outcomes across all channel integration scenarios and compare the resulting prices and profits. The analysis shows that a retailer with higher review quality has stronger incentives to adopt BOPS and charges a higher equilibrium price than under non-integration, while a firm with weaker reviews may gain by remaining separate to reduce direct competition. We also identify the cost thresholds that determine when BOPS adoption becomes profitable: rising operating costs weaken the adopter’s competitive advantage and consistently benefit the non-adopting rival. These results clarify how review heterogeneity shapes channel integration decisions and provide conditions under which BOPS adoption is strategically advantageous.