Quantum game analysis of green technology R&D cooperation between competing manufacturers under government subsidies

Driven by government subsidies, it's common for manufacturers to cooperate with their rivals in green technology research and development (R&D). However, the existing literature ignores the fact that, before cooperating, they still need to make independent investment decisions, and different cooperation forms have different cooperation closeness. We introduce the quantum game to consider these two factors. Specifically, the classical game model and quantum game model under green R&D subsidy and per-unit green product subsidy are constructed, we explore the optimal decisions, the influence of cooperation closeness on the optimal decisions and the expected profits, and how should the government design subsidies policy. We find that cooperating in a certain level of closeness and making green R&D investments and pricing decisions based on the cooperation closeness is more favourable. In the case of a large gap in green R&D capabilities, it is unwise for the stronger manufacturer to overly cooperate. The government should offer different levels and types of subsidies to the manufacturers according to the degree of competition and the cooperation closeness.