We consider a differential game model for a marketing channel formed by one manufacturer and one retailer. The latter sells the manufacturer's product and may also introduce a private label at a lower price than the manufacturer's brand. The aim of this paper is twofold. We first assess in a dynamic context the impact of a private label introduction on the players' payoffs. If this is beneficial for the retailer to propose his brand to consumers and detrimental to the manufacturer, we wish then to investigate if a cooperative advertising program could help the manufacturer to mitigate the negative impact of the private label.