The paper considers a dynamic game with a single manufacturer who supplies two retailers. The manufacturer determines his production rate of a specific product, the rate of quality improvement efforts as well as the rate of advertising for the product. Each retailer controls her purchasing rate and the consumer sales price. Payments from a retailer to the manufacturer are determined by a wholesale price or a revenue-sharing scheme. The retailers operate in the same consumer market in which they compete in prices for the consumer demand. Nash equilibrium conditions are derived and numerical methods are employed to characterize equilibrium behavior of the players in a differential game of fixed and finite duration.
EL OUARDIGHI, F., JORGENSEN, S. et PASIN, F. (2013). A Dynamic Game with Monopolist Manufacturer and Price-Competing Duopolist Retailers. OR Spectrum, 35(4), pp. 1059-1084.