To increase the sales of their products through advertising, firms must integrate their brand-advertising strategy for capturing market share from competitors and their generic-advertising strategy for increasing primary demand for the category. This paper examines whether, when, and how much brand advertising versus generic advertising should be done. Using differential game theory, optimal advertising decisions are obtained for a dynamic duopoly with symmetric or asymmetric competitors. We show how advertising depends on the cost and effectiveness of each type of advertising for each firm, the allocation of market expansion benefits, and the profit margins determined endogenously from price competition. We find that generic advertising is proportionally more important in the short term and that there are free-riding effects leading to suboptimal industry expenditure on generic advertising that worsen as firms become more symmetric. Due to free-riding by the weaker firm, its instantaneous profit and market share can actually be higher. The effectiveness of generic advertising and the allocation of its benefits, however, have little effect on the long-run market shares, which are determined by brand-advertising effectiveness. Extensions of the model show that market potential saturation leads to a decline in generic advertising over time.advertising, generic advertising, differential games, dynamic duopoly, optimal control

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We study a supply chain in which a consumer goods manufacturer sells its product through a retailer. The retailer undertakes promotional expenditures, such as advertising, to increase sales and to compete against other retailer(s). The manufacturer supports the retailer's promotional expenditure through a cooperative advertising program by reimbursing a portion (called the subsidy rate) of the retailer's promotional expenditure.To determine the subsidy rate, we formulate a Stackelberg differential game between the manufacturer and the retailer, and a Nash differential subgame between the retailer and the competing retailer(s). We derive the optimal feedback promotional expenditures of the retailers and the optimal feedback subsidy rate of the manufacturer, and show how they are influenced by market parameters. An important finding is that the manufacturer should support its retailer only when a subsidy threshold is crossed. The impact of competition on this threshold is nonmonotone. Specifically, the manufacturer offers more support when its retailer competes with one other retailer but its support starts decreasing with the presence of additional retailers. In the case where the manufacturer sells through all retailers, we show under certain assumptions that it should support only one dominant retailer. We also describe how we can incorporate retail price competition into the model.