Selecting after sales provider of complex product based on game and matching framework

As a strategic enabler of high-end manufacturing, the high-quality evolution of complex equipment is indispensable for any nation aspiring to industrial leadership. After sales service (AS) long relegated to a support function, which has emerged as a decisive determinant of product life-cycle value and, consequently, of this transformative journey. This study therefore investigates the technological innovation of AS for complex products through a Stackelberg game that captures the collaborative dynamics between an original equipment manufacturer (OEM) and an after-sales service provider (ASP). We derive the necessary and sufficient conditions under which an ASP finds participation economically viable, then embed these conditions into a multi-criteria matching framework that links ASP capabilities with spare-part requirements. Leveraging an entropy weighted DEMATEL (Decision-making Trial and Evaluation Laboratory) hybrid and we first quantify the causal salience of matching attributes and build a parsimonious evaluation index system. Next, by explicitly encoding bilateral attribute preferences, we formulate a two-sided matching model that identifies the Pareto-optimal ASP portfolio for any given product architecture. Finally, backward induction over the integrated game-matching structure yields a prescriptive tool that not only screens ASPs but also prescribes contractual levers to sustain long-term co-innovation. The proposed framework thus unifies strategic participation incentives with operational compatibility, offering OEMs a rigorous, implementable roadmap for selecting and governing after-sales partners in the era of servitized, high-stakes manufacturing.