Abstract: A marketing channel, where a retailer sells, its own store brand, along the manufacturer's brand, is considered.Competition exists between them.Each player invests in advertising in order to build the brand's goodwill, and the manufacturer bears part of the retailer's advertising investment We assume that the retailer's advertising promotion has a negative impact on the goodwill of manufacturer's brand A methodology of differential games is adopted to investigate the optimal advertising strategies of the manufacturer and the retailer in Stackelberg leacler-follower game under a dynamic circumstance.The effect of the parameters of the manufacturer and the retailer on the optimal decision is analyzed.Finally, we prove that the decision of Stackelberg leacler-follower game is prior to the one of Nash non-cooperative game.

Key words: supply chain, Stackelberg game, differential game, store brand, cooperative advertising