Game theory model for the effects of government subsidies on pricing decisions of the closed-loop channel

To investigate the effects of government subsidies on the pricing decisions of the forward and reverse channels, using game theory, we consider a government who has three options for subsidies that are paid solely to the retailer, solely to the manufacturer, or shared between the manufacturer and the retailer. Then we compared these three subsidies approaches with no subsidies. It shows that: (1) there is no effects on the pricing decisions of the forward channel whether pay subsidies or not, (2) the manufacturer’s and the retailer’s profits under three kinds of subsidies are higher than that of no subsidies, (3) the unit subsidy that the government pays to the manufacturer or the retailer is equal, which is twice than that of simultaneously pays to the manufacturer and the retailer.