Smart Connected Products (SCPs) and Digital Services (DSs) play pivotal roles in facilitating the digital and intelligent transformation of the manufacturing industry. In the context of the service-oriented transformation of manufacturing, SCPs are sold by Original Equipment Manufacturers (OEMs) via a retailer, whereas DSs are either provided directly by OEMs or indirectly through the retailer, thereby forming a product-service supply chain. This paper constructs a three-stage dynamic game model and analyzes two DS strategies, i.e., integrated and separated DS strategies, for competing OEMs by integrating and separating manufacturing and DS departments. These strategies encompass four scenarios: both OEMs integrate them, both separate them, and one OEM integrates while the other separates them. We analyze the equilibrium DS levels, the prices of SCPs and DSs, demands, and profits in four scenarios, and explore the service and pricing decisions of supply chain members at equilibrium. The results indicate that OEMs can achieve higher profitability by separating manufacturing and DS departments as competition intensity increases within a certain range. Secondly, when both OEMs adopt the same strategy, integration of departments is more profitable if competition is low, whereas separation yields higher profits when competition is intense. Interestingly, two Nash equilibria emerge: an OEM achieves the highest profit by adopting an integrated DS strategy in an asymmetric scenario when competition is weak and digital R&D is challenging. Conversely, both OEMs can reach a Nash equilibrium by separating their departments when competition is intense and digital R&D is relatively simple. Thirdly, from the perspective of the retailer and the entire supply chain, integrating manufacturing-service at both OEMs provides the highest return when competition is low. However, under intense competition, the highest profits are achieved when OEMs adopt different DS strategies. Finally, in a highly competitive market without a retailer, an asymmetric scenario proves most profitable when digital R&D investment is low, whereas separating manufacturing-service yields the highest profits when digital R&D investment is high.
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