Complexity of a two-stage R&D game within a cluster supply chain considering vertical R&D spillovers, effective information, and government subsidies

In the research on spillover effects in supply chain game models, most studies are based on complete rationality or consider horizontal spillovers between enterprises, while neglecting vertical spillovers between upstream and downstream enterprises in the supply chain R&D game with bounded rationality. This paper creatively proposes a two-stage cluster supply chain game model that includes vertical R&D spillovers, effective information, and government R&D subsidies. In the product development stage, the supplier and manufacturer use rational estimation and GD mechanisms to conduct R&D simultaneously, taking R&D efforts as a decision variable. In the Stackelberg-Bertrand stage, the supplier and manufacturer successively determine the wholesale price and retail price. Results show that: first, the more effective information the R&D enterprise has, the more conducive it is to the stability of R&D efforts; second, under certain circumstances, R&D subsidies and vertical spillovers may lead to instability in R&D process, while higher R&D costs are conducive to the stable balance of R&D in the supply chain.