Co‐Op Advertising in Dynamic Retail Oligopolies

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.