A nearly explicit feedback Stackelberg-Nash equilibrium is obtained in a dynamic distribution channel consisting of a manufacturer and two competing asymmetric retailers engaged in promoting the manufacturer's product to be sold through the retailers. The manufacturer decides on its support for the retailers' advertising activities by announcing cooperative advertising subsidies called "participation rates." The retailers compete for market share by selecting advertising efforts. We formulate the problem as a Stackelberg-Nash differential game and reduce it to merely solving a set of algebraic equations. We find that the manufacturer should offer the cooperative advertising policy to only one retailer and even then, only when a "participation threshold" depending on the model parameters is exceeded. We identify the levers that determine the optimal participation rate. Furthermore, we obtain important insights into how sensitive the optimal solution is with respect to the parameters. Moreover, we show that retail-level competition induces the manufacturer to offer a higher level of support to the supported retailer and over a wider range of parameters when compared to the results obtained in a one-manufacturer, one-retailer setting studied in the literature.