Separation or integration: The game between retailers with online and offline channels

•We examine the competition between two retailers with both online and offline channels.•Two retailers simultaneously decide whether to adopt a separation strategy or an integration strategy.•We derive the optimal pricing strategies of retailers under four possible scenarios.•The prisoner's dilemma is discussed when neither retailer offers a BOPS channel.•We explore the impact of unit delivery costs for fulfilling online orders on the retailers’ decisions when considering endogenous shipping fees charged to consumers.