Infinity Period Dynamic Control of a Kind of Channel’s Price and Brand Investment: A Differential Game Method

The infinity period dynamic control problem of distribution channel was studied with differential game approach. Four differential dynamic control models of coordinated channel game, uncoordinated static game, Stackelberg game with manufacture controlled, and Stackelberg game with n retailers controlled were constructed. Some results applied dynamic optimization theory made with Hamilton function. The conclusions are as follows. (1) Optimization brand investment controlled by manufacture has nothing to do with time. (2) Retail price was the most minimum when channel was integrated. (3) Manufacture’s profits of uncoordinated static game and Stackelberg game with manufacture controlled were more than Stackelberg game with n retailers controlled. (4) Retailer’s profits of Stackelberg game with n retailers controlled were less than Stackelberg game with manufacture controlled. (5) Channel’s total profits of Stackelberg game with n retailers controlled were the most minimum.