Modelling cooperative advertising decisions in a manufacturer-distributor-retailer supply chain using game theory

This work considers cooperative advertising decisions in a manufacturer-distributor-retailer supply chain, where the manufacturer is taken as the Stackelberg leader, using differential game theory. The distributor and retailer are the first and the second followers, respectively. We introduce the distributor into the traditional manufacturer-retailer channel through his direct involvement in advertising as being incorporated into the non-stochastic Sethi's sales-advertising dynamics. This is used to model the awareness share dynamics in which the distributor and the retailer directly engage in advertising, while the manufacturer bypasses the distributor to subsidise only the retail advertising effort. We consider a subsidised and unsubsidised channel structures, where each structure results in a system of three nonlinear equations, which cannot be solved analytically, but only numerically. However, we show that the unique solution to each of the systems exists, provided certain conditions are satisfied. The distributor and the retailer's advertising strategies are developed for both when subsidy is provided and when it is not provided. We also obtain the manufacturer's subsidy rate and the market awareness share for both when retail advertising is subsidised and when it is not subsidised. We observe that with the provision of subsidy, the distributor reduces his advertising effort. However, the resulting increase in the retail advertising effort is larger than the reduction in the distributor's advertising commitment, thus making the channel advertising effort larger with subsidy. It further shows that to avoid being shortchanged, each player should adopt only his optimal strategy or strategies as the case may be.